This is, rather obviously, never clarified by Tolkien. Primarily because there was no need to, in the same way it isn't clarified for Dwarves (recall Tolkien's "joke" in Appendix A: "This has given rise to the foolish opinion among Men that there are no dwarf-women, and that the Dwarves ‘grow out of stone’") or Elves, only presumed.
Instead I will paint a picture of what the Ents were like and allow you to come to your own conclusion. Firstly, Ents were far more "humanoid" than is commonly thought. Treebeard likened the similarity between Ents and their trees to shepherds and their sheep:
Sheep get like shepherd, and shepherds like sheep, it is said; but slowly, and neither have long in the world. It is quicker and closer with trees and Ents, and they walk down the ages together...
The Two Towers, Book III, Chapter 4: “Treebeard”
Treebeard clarifies that these similarities might've grown more pronounced for the Ents and their trees as they have walked "ages together" unlike the shepherds of Men who lived no longer than a century. This would suggest that they were mostly humanoid although resembled trees. A bit like a dog owner and their dog.
Secondly, while Treebeard's skin is described as bark-like, it is explicitly described as being smooth, like human skin:
Whether it was clad in stuff like green and grey bark, or whether that was its hide, was difficult to say. At any rate the arms, at a short distance from the trunk, were not wrinkled, but covered with a brown smooth skin.
Thirdly, Ents are described (repeatedly) to be rather troll-like, one example from earlier in the above quote:
They found they were looking at a most extraordinary face. It belonged to a large Man-like, almost Troll-like, figure, at least fourteen foot high, very sturdy, with a tall head, and hardly any neck.
Finally, how Ents came to be, what they 'are', I have emphasised the parts that really need to be read, the rest is contextual:
All have their worth,' said Yavanna, '... But the kelvar can flee or defend themselves, whereas the olvar that grow cannot. And among these I hold trees dear. Long in the growing, swift shall they be in the felling, and unless they pay toll with fruit upon bough little mourned in their passing. ... Would that the trees might speak on behalf of all things that have roots, and punish those that wrong them!'
'This is a strange thought,' said Manwë.
And Manwë said: 'O Kementári, Eru hath spoken, saying: "... Behold! When the Children awake, then the thought of Yavanna will awake also, and it will summon spirits from afar, and they will go among the kelvar and the olvar, and some will dwell therein, and be held in reverence, and their just anger shall be feared. ..."
The Silmarillion, Chapter 2: “Of Aulë and Yavanna”
Ents therefore have fëar and as such are sentient beings. Whether this affects their reproduction is anyone's guess. But it is clear they have free will and as such most likely wouldn't reproduce through the rather passive means that are usually expected of a tree.