Schilling has been sidelined with a sore shoulder and the Red Sox have decided to be conservative in bringing him onto the roster. He is eligible to return from the disabled list July 4, but Francona said it will be pushed back at least a week.
Boston entered play Wednesday with a 10-game lead in the American League East.
"He can throw now, but I think they (doctors) want him to reach certain levels with the testing," Francona said. "We want him to finish the season in good condition. That's why we're trying to be safe. Sometimes it's tough to be safe."