The tweet, which has since been deleted, features a cartoon drawing of Javid, who replaced Amber Rudd as home secretary after she stepped down last weekend over the Windrush scandal.
Next to Javid in the cartoon is a board headed “targets” and the overhead caption reads: “I just want to settle in, get organized, then deport my parents.”
The cartoon sparked outcry, with Tory MP Sarah Wollaston telling Lord Adonis that there was “no excuse of this deeply offensive personal insult targeting” of her colleague.
Cabinet minister Penny Mordaunt also rounded on Lord Adonis, saying the tweet displayed “profoundly poor judgement”.
LBC radio host Maajid Nawaz said he was “appalled” that Lord Adonis “could endorse the racist hounding of” Javid.
Javid responded directly to Lord Adonis, writing on Twitter “you’re better than this”.
Former education minister Lord Adonis later deleted the tweet and apologised to Javid for the “poor taste” cartoon.
Lord Adonis wrote: “Sajid, on reflection I think the cartoon is too personal and in poor taste. I have deleted it. I am sorry. Andrew.”
Javid, who is the son of a Pakistani bus driver, banned the phrase “hostile environment” in relation to enforcing immigration laws after he became home secretary last week.
Just hours after replacing Rudd, the Tory minister sought to reassure MPs that incidents like the Windrush debacle would not happen on his watch and repeatedly referred to himself as a “second-generation migrant”.
He said he was “personally committed and invested” in setting right the procedures which saw people who had lived in the UK all their adult lives face deportation.
But his move to use the phrase “compliant environment” instead was criticised by Labour MP David Lammy in the Commons last week.
Lammy accused Javid of using the language of slave owners and fascists by insisting illegal immigrants should be subject to a “compliant environment”.