Texans coach Bill O'Brien had acknowledged on Monday that Johnson would be sidelined for "a lot of time."
Sunday's concussion was the 2015 first-round pick's second in less than a month, as he also left the Texans' Aug. 18 preseason game against the San Francisco 49ers after hitting his head on the field.
Johnson struggled in the Texans' season opener before he left with the concussion, rankings 91st out of 99 cornerbacks in Week 1, according to PFF. He had four combined tackles.
The Texans do not have depth at cornerback. In Johnson's absence, Aaron Colvin will likely see more playing time outside alongside Johnathan Joseph. On Monday, O'Brien said moving safety Kareem Jackson back to cornerback is a possibility, but that it's a hard decision to make because the veteran played so well at his new position on Sunday.
Houston also has cornerback Kayvon Webster on the roster, who is currently rehabbing from injuring his Achilles last December with the Rams. O'Brien said Webster won't be back for Week 2, but he's "trending in the right direction" and he will be part of the cornerback rotation once he is healthy.
The Texans also have cornerback Johnson Bademosi on the roster, but he was signed to primarily play special teams and he did not play a snap on defense against the Patriots.
Johnson played in just 12 games total in 2017 and 2018 and had 45 combined tackles and two passes defended.
The Texans also lost starting right tackle Seantrel Henderson for the season in the 27-20 loss to the Patriots with an ankle injury.
ESPN's Sarah Barshop contributed to this report.