Here is a partial answer to my own question:
Zeiss Ikon's answer says that there was lower gravity on the Moon in Heinlein's Have Spacesuit, Will Travel (1958).
In the movie, Destination Moon (August, 1950) (transcript):
Doc, I'll never get use to this.
This must weigh 500 or 600 pounds!
On Earth it does. Gravity here
is about 1/6 as much.
That means things weigh 1/6 as much.
I know it, but I can't believe it.
By coincidence the comment of marecllothearcane says:
Destination Moon (the Tintin comic), published 30 March 1950, shows lower surface gravity on the moon.
Added 11-13-*19. The children's novel The Voyage of the Luna 1 (1948), by David Cragie (Dorothy Glover), Part Two, Chapter IX, "The New World", page 176:
The force of gravity on the moon being only a sixth as great as on the earth, they could jump six times as high as they were accustomed to, and they were to discover later that they could climb six times as high without getting tired; but as this stage of their adventure it was still part of the great mystery.
The comment of Drewbenn about The Moon Maid (1926):
The Moon Maid, available through Project Gutenberg, is easy to check, and the characters are well aware of it: "...the natural effects of the lesser gravity of the Moon. We have discussed the matter upon many occasions... yet when we faced the actual condition we gave it no consideration whatsoever. Of course, it's in the context of jumping over a river. So you can remove everything in your question that comes after that
H.G. Wells' The First men in the Moon (1900,1901) Chapter 9, "Prospecting Begins", at Project Gutenberg, says:
As he stepped forward he was refracted grotesquely by the edge of the glass. He stood for a moment looking this way and that. Then he drew himself together and leapt.
The glass distorted everything, but it seemed to me even then to be an extremely big leap. He had at one bound become remote. He seemed twenty or thirty feet off. He was standing high upon a rocky mass and gesticulating back to me. Perhaps he was shouting—but the sound did not reach me. But how the deuce had he done this? I felt like a man who has just seen a new conjuring trick.
In a puzzled state of mind I too dropped through the manhole. I stood up. Just in front of me the snowdrift had fallen away and made a sort of ditch. I made a step and jumped.
I found myself flying through the air, saw the rock on which he stood coming to meet me, clutched it and clung in a state of infinite amazement.
I gasped a painful laugh. I was tremendously confused. Cavor bent down and shouted in piping tones for me to be careful.
I had forgotten that on the moon, with only an eighth part of the earth’s mass and a quarter of its diameter, my weight was barely a sixth what it was on earth. But now that fact insisted on being remembered.
So the search should be for examples published in or before 1900.
[Added 08-04-2019. Edgar Allen Poe's The Unparalleled Adventure of One Hans Pfaall, published in 1835, is mentioned as a possibility by Sean Condon in his answer, although he was a little uncertain how to interpret Poe's words.
I known of another Poe work, published years later, that is a bit more specific about the lunar gravity, "Mellonta Tauta" published in Godey's Ladys's Book, February, 1849, and allegedly written in 2848, which includes this paragraph:
April 7.—Continued last night our astronomical amusements. Had a fine view of the five Neptunian asteroids, and watched with much interest the putting up of a huge impost on a couple of lintels in the new temple at Daphnis in the moon. It was amusing to think that creatures so diminutive as the lunarians, and bearing so little resemblance to humanity, yet evinced a mechanical ingenuity so much superior to our own. One finds it difficult, too, to conceive the vast masses which these people handle so easily, to be as light as our own reason tells us they actually are.
The last sentence seems to be referring to the lower surface gravity on the Moon.
Of course that may not matter since user14111's answer mentions two earlier stories that have people jumping long distances in the lighter lunar gravity.
They are A Voyage to the Moon, by George Tucker (1827) and The Man in the Moone, by Bishop Francis Godwin (1638). Yes, 1638. As user14111 says, Godwin exaggerated the difference in surface gravity but can be forgiven since he wrote before Isaac Newton was born.
It is possible that user14111 found the earliest example, but not entirely certain.
One good candidate to be the earliest work of science fiction to mention the lower surface gravity of the Moon would be Johannes Kepler's (1571-1630) Somnium.
Somnium (Latin for "The Dream") is a novel written in 1608, in Latin, by Johannes Kepler. The narrative would not be published until 1634 by Kepler's son, Ludwig Kepler. In the narrative, an Icelandic boy and his witch mother learn of an island named Levania (our Moon) from a daemon. Somnium presents a detailed imaginative description of how the Earth might look when viewed from the Moon, and is considered the first serious scientific treatise on lunar astronomy. Carl Sagan and Isaac Asimov have referred to it as one of the first works of science fiction.
Somnium began as a student dissertation in which Kepler defended the Copernican doctrine of the motion of the Earth, suggesting that an observer on the Moon would find the planet's movements as clearly visible as the Moon's activity is to the Earth's inhabitants. Nearly 20 years later, Kepler added the dream framework, and after another decade, he drafted a series of explanatory notes reflecting upon his turbulent career and the stages of his intellectual development. The book was edited by Ludwig Kepler and Jacob Bartsch, after Kepler's death in 1630.
Since Somnium was written in stages, it may be uncertain precisely when various details about the Moon were first included, but it was first published four years before Godwin's book.
So there is a factual question of whether Somnium mentions lower surface gravity on the Moon, and a more subjective question whether one considers Somnium to be an early work of science fiction.
If the answer to both questions is yes, then there should be only a few earlier stories of voyages to the Moon, back to Lucien's True History, to consider as possible candidates.]