Bowe had been training with Ireland ahead of their victory over Italy on Saturday and it was believed he could be in the frame for a return to international again this weekend.
But team manager Mick Kearney confirmed Bowe would be released back to his club for their match on Friday night, with Andrew Trimble likely to continue on the wing.
Peter O'Mahony is expected to be fit after missing the win over Italy while Cian Healy is also likely to be fit after suffering an ankle injury against Italy.
"Peter O'Mahony has made an excellent recovery from his hamstring strain and is expected to train fully this week," said Kearney.
"As a precaution he (Healy) was put in a boot overnight. We expect Cian will train tomorrow and Conor Murray's tummy bug has settled."