Shueb Salar is alleged to have posted abusive language about women and homosexuals on Twitter, in 2012.
An investigation will be carried out into the "serious issues", said a spokesman for Labour candidate Mr Khan, an ex-shadow minister.
Mr Salar, who has not commented, started working for Mr Khan in 2014.
In light of the posts, cabinet minister Chris Grayling questioned Mr Khan's judgement in employing Mr Salar.
"'These comments have absolutely no place in modern society," the leader of the House of Commons said.
"The mayor of London makes a large number of decisions about who to hire and how to spend public funds: his record shows Sadiq Khan can't make those decisions in a way that stands up for Londoners."
Mr Khan is tipped by the bookies to become London's next mayor on 5 May, beating his Tory rival Zac Goldsmith.
A spokesman said: "Clearly these are serious issues. Shueb Salar has been suspended from Sadiq Khan's parliamentary office pending an investigation."

Joe Pugh, 18, and his girlfriend Leah Washington, aged 17, both of Barnsley, were riding on the Smiler on Tuesday.
Two carriages crashed on the ride at the Staffordshire theme park, leaving some passengers trapped for four-and-a-half hours about 25ft (7.6m) up in the air.
Mr Pugh and Miss Washington and another man and a woman suffered leg injuries.
A man who operated the Smiler ride when it opened in 2013, who gave his name only as Mark, has expressed his frustration the accident happened.
Meanwhile, Oaks Working Men's Club, in Barnsley, where Mr Pugh works said: "We at The Oaks WMC would like to extend our prayers and best wishes in the speedy recovery of our barman Joe Pugh and his girlfriend Leah Washington."
Mr Pugh's friend Alice Holmes spoke of her shock to the BBC's Mark Ansell.
She said: "I text saying 'Are you ok? Smiler has crashed' and I never got a reply.
"I text him again and again and he still didn't reply. Then, this morning I saw a clip on the news and I knew it was him from his outfit because he dresses quite nice."
The BBC's Declan Wilson spoke to friends of Miss Washington, who said she was the more badly injured.  One friend said she had injuries to her legs, hips and hands.
Alton Towers said on social media that the park would remain closed on Thursday, as an investigation into the cause of the accident continued.
Nick Varney, chief executive of the park's owners Merlin Entertainments, said: "A full investigation is now under way and we will continue to work closely with the emergency services and the Health and Safety Executive to better understand the cause of this terrible accident."
The accident happened at around 14:00 BST on Tuesday, leaving 16 people stuck in the air at an angle of about 45 degrees.
The park said the carriage carrying the people was travelling at 20mph when it crashed.
Four people were airlifted to major trauma centres across the West Midlands.
People at the theme park reported hearing "a loud crash" when the collision happened.
Mr Pugh, a textile design student at the University of Huddersfield, has been sent supportive messages on social media from friends.
"Wishing Joe Pugh and his girlfriend a speedy recovery," Kay Eggleston wrote.
Ross William Gibson wrote: "Can't believe when I wrote this I didn't know one of the four was my friend Joe Pugh and his girlfriend. Get well soon pal."
Mark, who operated the Smiler ride in 2013, said: "I am frustrated that such a simple error has been made, knowing myself how the system should function and that it is one of the safest rides I've ever worked on.
"One carriage should only be in a certain block section at a time.
"When the empty carriage didn't make it to the next block section after a certain amount of time, the ride should have stopped any other carriages being sent and entering that block."
One of London mayoral hopeful Sadiq Khan's aides has been suspended after offensive social media messages were published.
[NEXT_CONCEPT]
Two teenagers have been named as victims of the Alton Towers rollercoaster accident.