Ospreys wing Bowe is struggling with a knee problem while Leinster's Heaslip is nursing an ankle injury. The race is now on for them to return against France on February 13.
The duo that flourished with the Lions in South Africa have established themselves as two of Ireland's most consistent performers and their loss will be a major set-back to Declan Kidney's Six Nations plans.
"You never like to see guys injured - we know how much playing for Ireland means to those guys," said Kidney.
"We've tried to build a squad over the last few years and this will be the test of that.
"I have a huge belief in the way Irish rugby comes from the grass roots up. Of course there won't be as much video analysis on the new guys so that will be an advantage."