Choudhury apologised this week and Leicester manager Brendan Rodgers said his player was genuinely remorseful.
"They do not represent my true beliefs," England Under-21 international Choudhury said in a statement.
"I've learned a lot as a person in my early years as a professional - certainly enough to know that some of the thoughtless comments I have made in the past are both hurtful and offensive.
"I'm deeply sorry to anyone I have offended - both at the time and since they've been recirculated."
The FA said the comments constituted an "aggravated breach" as they included reference to ethnic origin and/or race and/or sexual orientation.
Choudhury has made 10 appearances for Leicester this season and started for the first time under Rodgers in their 3-0 Premier League victory over Arsenal last weekend.
He has until May 13 to respond to the charge.
(Reporting by Hardik Vyas in Bengaluru, editing by Ed Osmond)
