Houston television station KRIV reports that Williams walked by himself Thursday morning at Presbyterian Hospital in Dallas.
He suffered a cracked vertebra and severe ligament damage in his neck Aug. 22 during a preseason game against the Dallas Cowboys.
Williams told the station, "I started walking today. I brushed my own teeth today, sat up in a chair today, fed myself today.
"I'm doing good, man."
Doctors say it is unlikely he'll be able to play football again, something the 26-year-old says he accepts.
"I'm mad that I won't be able to play football again, but I'll get over it," Williams said, according to the Houston Chronicle. "I feel blessed, truly blessed, because I'll be able to walk again and lead a normal life."
Before Thursday night's preseason game against Tampa Bay, the Texans honored Williams, the team's best special-teams player, by having the kicking team introduced, according to the Chronicle. Kicker Kris Brown, the last player introduced, ran onto the field holding up Williams' No. 86 jersey.
"I feel so blessed right now," Williams said, according to the Chronicle. "I feel so loved."
According to the report, Williams' teammates have been in nearly constant contact with him since he was injured. He said he greatly appreciates that support.
"That shows what football's all about -- camaraderie and relationships that'll last for the rest of your life," he said, according to the report. "It shows we're a family, and we're going to stick by each other no matter what."
The Associated Press contributed to this report.