The message, posted on the Leeds North West Lib Dem account at around 10.30pm on Tuesday night, was widely shared on Twitter before it was deleted.
An apology later posted on the same account read: "Apologies for the last tweet. Our account was compromised."
Replying to the explicit invitation, Mr Mulholland wrote: "next time, can it say 'have a few drinks, see you we get on, go out a few times & take it from there?" I'm old fashioned!'"
Mr Mulholland later posted: "Night all. If suddenly my account starts tweeting obscene and offensive things, it's been hacked. Probably."
The MP told followers the explicit message could not have been posted by him as it used the word "wanna" and he dislikes Americanisms.
The most famous Yorkshire political Twitter blunder remains Ed Balls accidentally posting his own name as he tried to search for references to himself.
It continues to be celebrated annually on "Ed Balls Day".