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."
One of London mayoral hopeful Sadiq Khan's aides has been suspended after offensive social media messages were published.