Williams returned to practice on Monday, but said he will likely have to deal with the injury -- plantar fasciitis -- all season.
"It's a situation where I don't think it's going to go away until maybe the offseason," Williams said. "We're just going to deal with it and try and grin and bear it."
Williams saw a specialist last week and did not play in the preseason game against Dallas on Saturday night. He will almost assuredly sit out the preseason finale against Houston on Thursday night to rest up for the season opener at San Diego on Sept. 11.
That is if Williams is not suspended for the game stemming from a test for a banned stimulant three years ago. Williams lost a court battle with the NFL over the test, but has yet to be notified if he will be eligible to play when the season begins.
Williams said he felt a little better running around during a light practice on Monday.
"I ran pretty good," Williams said. "It wasn't real physical. It was a lot of hand work and running. It wasn't too bad. I needed to run."
With his versatility as both a pass rusher and run stopper, the former All-Pro tackle is critical to the Vikings' defense. Coach Leslie Frazier said he is "pretty optimistic" that Williams will be ready physically when the season starts.
"He moved around fairly well," Frazier said. "Much better than I anticipated."
Tight end Visanthe Shiancoe (hamstring), linebacker Jasper Brinkley (hip) and cornerbacks Asher Allen (toe), Chris Cook (hamstring) and Devon Torrence (quadriceps) also will not play against the Texans because of injuries.
Frazier said Brinkley was sent to a specialist to examine his hip flexor, and the team moved defensive end Everson Griffen to linebacker for some drills to try to address the lack of depth. Griffen is in his second year out of USC, and Frazier said the Vikings like his chances for making the transition and giving them some much-needed flexibility.
"He's just a tremendous athlete with good football intelligence," Frazier said. "He has some playmaking abilities, so we want to utilize his athletic ability."