Escobar suffered a right shoulder injury in the third quarter of Saturday's 37-30 loss to the Baltimore Ravens after laying out for a 37-yard completion.
He will be examined further Sunday.
"We don't think it's going to be too, too serious," coach Jason Garrett said.
Linebacker DeVonte Holloman left in the fourth quarter with a neck injury. There is concern because Holloman missed seven games as a rookie last season with a neck injury. He was able to return and start the final two games.
He has been playing mostly at backup middle linebacker in training camp.
"We don't know if it's the exact same thing, but it's the same body part so we're checking on him [Saturday] night and we'll check him out in the morning," Garrett said.