Bergwijn suffered an ankle injury during Saturday's 1-1 draw with Burnley at Turf Moor.
He joins fellow attackers Harry Kane and Heung-min Son on the sidelines.
"Steven, I don't expect him to play this season," Mourinho said. "Can I believe it? Yes, I can.
"I have never known it like this, especially speaking about traumatic injuries. Only Harry Kane's injury was not a traumatic injury but a typical injury of the December period in the Premier League.
"We were psychologically more down with the other injures. This one, from three, four or five to six or seven is the same. No problem."