Mr Corbyn had imposed a three-line whip on his MPs to vote to back Brexit.
But 52 Labour MPs rebelled in Wednesday's vote, including 11 junior shadow ministers and three whips, whose job it is to impose party discipline.
Clive Lewis, who quit the shadow cabinet over the vote, said rumours of a leadership bid by him were "fantasy".
Mr Corbyn imposed the three-line whip after vowing his party would not seek to obstruct the implementation of the EU referendum result.
Convention dictates that members of the leader's shadow cabinet team should resign or be sacked if they defy such an order.
Some did resign but the remaining rebels are to receive only a letter insisting that they must comply with the whip in the future.
The decision not to sack them leaves Labour facing the prospect of three whips trying to persuade their colleagues to vote with a leader who himself rebelled against Labour more than 400 times - when they have defied him themselves, BBC political correspondent Chris Mason says.
Mr Lewis has since been replaced as shadow business secretary by Rebecca Long-Bailey.
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