According to coach Mike Sullivan, Crosby is being evaluated for an upper-body injury.
Crosby tallied a goal and an assist with a plus-4 rating in a 4-0 victory over the Coyotes on Saturday.
Crosby scored a goal and added an assist in Tuesday's 6-3 loss to the Islanders.
Crosby is still searching for his first goal of the 2018-19 campaign, but he does have four assists through five games.
Crosby has two assists in Saturday's 7-3 preseason triumph over Columbus.
Crosby recorded a goal and an assist in Tuesday's 4-3 Game 3 loss to the Capitals.
Crosby registered a goal, an assist and five shots during Friday's 4-3 overtime loss to New Jersey.
Crosby collected two assists during Tuesday's 6-3 win over Ottawa.
Crosby dished out three assists in Thursday's 6-3 doubling up of Minnesota.
Crosby garnered an assist against Carolina on Tuesday, extending his streak of consecutive games with at least a point to eight.