The Chilean international was lacking match fitness after signing on the final day of the summer transfer window from Mexican side Club America.
Now, Alex McLeish's £3.3million capture is sidelined with a knee ligament strain.
McLeish had hoped Beausejour would be fit to return following the international break after being left out of the home clash with Everton last weekend. But he needs more rest and recuperation and will not be risked at the Emirates Stadium.
McLeish said: "Jean came to us half fit and hadn't played many games and that is part of the problem when you sign players right at the end of the transfer window.
"Now he's strained his medial ligament and we have to make sure we don't take any unnecessary risks with him.
"He needs to rest to make sure he is right and he won't be available next weekend."