A few years ago, considerable research was done into Khan, the development of his character, and the making of "Space Seed" by sociologists Maria Jose and John Tenuto, leading to a six-part interview with them by the official Star Trek web site.
From The Evolution of "Space Seed", Part 5, we have the following notes regarding the costuming for the episode:
The costumes of the original Star Trek were largely the result of the talents of William Ware Theiss... He had served for four years in the United States Navy before turning his attention to costume design.
Like all artists on Star Trek, Theiss had to regularly deal with many limitations, including budget, time and network rules, and "Space Seed" was a unique challenge. The costumes had to demonstrate the regality of Khan that was familiar to the audience, yet also be futuristic in their design.
Despite these limitations, Theiss’ output on "Space Seed" is remarkable for its iconic nature and its interesting symbolism...Theiss’ three original designs all have a common element: ovals. Khan's cryogenic outfit is entirely constructed of these ovals, interlocking together symbolically to mimic perhaps DNA helix strands...The interconnecting ovals again appear on Khan’s dress dinner jacket, a design that showcases Montalban’s physique and Khan’s superiority.
The tunic / dinner jacket is an original construction by Theiss, designed to display royalty and futuristic notes at the same time, as mentioned above. That is to say, it is not exactly an existing Earth garment.
But given Khan's ethnic origins in the Indian subcontinent, Theiss likely took some inspiration from traditional dress of that region, namely the achkan, Nehru jacket, and sherwani, as others have noted.
There also exist action figures of Khan wearing the tunic:
Unfortunately, the packaging for the figures doesn't have anything to say about the tunic.
Finally, as for purchasing a (life-size) version of the tunic, it doesn't seem to be a particularly popular item. I cannot find a vendor that has made exact replicas of it. Furthermore, the current location of the actual tunic worn on set by Ricardo Montalbán is unknown. (This is in contrast to his cryogenic-sleeper suit, which has been auctioned several times — see the Star Trek Prop & Costume Authority.)