MP Andre Lebedev is not just asking whether Mr Ilyumzhinov is fit to govern.
He is also concerned that, if he was abducted, he may have revealed details about his job and state secrets.
The MP has written a letter to Mr Medvedev raising a list of his concerns.
In his letter he says that - assuming the whole thing was not just a bad joke - it was an historic event and should have been reported to the Kremlin.
He also asks if there are official guidelines for what government officials should do if contacted by aliens, especially if those officials have access to state secrets.
Actually there are guidelines for alien contact. If you are curious, you can find the set of post-detection protocols here (yes, it does mostly focus on SETI) and the list of people on the committee here. The chair of the committee is Paul Davies (he was our Science & Religion speaker in 2008).
In any case, back to aliens. Well, it's quite possible that aliens picked Kalmykia's Ilyumzhinov because of chess. After all, and lets be honest here, there is a good possibility that these star-hopping aliens will also be...nerds:
[Ilyumzhinov] has been president of Kalmykia, a small Buddhist region of Russia which lies on the shores of the Caspian Sea, for 17 years.
The millionaire former businessman has a reputation as an eccentric character.
As president of the World Chess Federation, he has spent tens of millions of dollars turning the impoverished republic into a mecca for chess players - building an entire village to host international tournaments.
Read the full story here.