Ms Abbott missed a vote on the EU exit last week in Parliament, citing a migraine – despite Mr Corbyn calling a three-line whip on the issue.
The shadow home secretary is a Corbyn loyalist but is also an avowed europhile and has regularly championed the EU and the single market.
MPs are set to vote on Wednesday night on the bill which allows Article 50 to be triggered.
Responding to a call from Tory MP Karl McCartney for a show of support over Brexit, Mrs May said: “The country wants us in this house to unite behind the Government’s work to ensure that we get the best possible deal for the United Kingdom as we leave the European Union.”
Turning to her beleaguered opposition, Mrs May said: “I had hoped that I was going to able to welcome the shadow home secretary to the front bench in time for the vote which takes place later tonight.
Theresa May mocked Diane Abbott and Jeremy Corbyn over Labour's woes
“Perhaps members of the Labour Party are starting to realise that the only real headache is their leader.”
Ms Abbott was accused of cowardice and “bottling it” over the vote last week, with several MPs suggesting she should consider her position.
Overnight speculation mounted Mr Corbyn could be considering his resignation as Labour leader.
In a number of tweets early on Wednesday morning, Jennifer Williams, the Manchester Evening News’ social affairs editor, said Mr Corbyn had settled on a departure date.
However, those close to Islington North MP have dismissed the reports and said “someone is spreading mischief”.
Some 47 pro-Remain Labour MPs defied the leadership to oppose the European Union (Notification of Withdrawal) Bill at second reading and Mr Corbyn is expected to face a renewed wave of defiance.
Diane Abbott and Jeremy Corbyn are close allies and used to be romantically involved
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Perhaps members of the Labour Party are starting to realise that the only real headache is their leader
The Labour leader is imposing a three-line whip on the vote at the third reading – a move that risks the resignation of high-profile shadow cabinet ministers like Clive Lewis.
Last week three other members of the shadow cabinet, shadow environment secretary Rachael Maskell, shadow Welsh secretary Jo Stevens and shadow equalities minister Dawn Butler, resigned to oppose the Bill.
As well as 10 junior shadow ministers, three whips also voted against the Bill.
MPs are expected to debate the Bill allowing Article 50 to be triggered for up to seven hours, with the final vote expected to be held at around 8pm.
The Government comfortably defeated attempts on Tuesday night to give MPs a decisive say over the final terms of Brexit, despite anger among Tory remain campaigners.
Seven Conservative MPs, Ken Clarke, Bob Neill, Andrew Tyrie, Claire Perry, Anna Soubry, Antoinette Sandbach and Heidi Allen, defied their party whip.
But their protest was virtually cancelled out by six Labour MPs, Frank Field, Ronnie Campbell, Kate Hoey, Kelvin Hopkins, Graham Stringer and Gisela Stuart, who voted with the Government.