Johnson will miss his fifth consecutive game since suffering a right hamstring injury during the Texans' Week 4 game against Pittsburgh. The injury required minor surgery two days later.
"Obviously, he's not ready to go yet," Kubiak said. "When he got pushed Monday, the response was, 'No, not yet.'
Johnson has been sore since working out on Monday, and it's possible the Texans will hold him out until their bye. After playing the Browns, the Texans travel to Tampa on November 13 and have the following week off.
Houston is 5-3 this season, including 2-2 since Johnson has been sidelined.
Johnson had 25 catches for 352 yards and two touchdowns in the first four games this season. He has scored 52 touchdowns and racked up 9,516 receiving yards since 2003.