Sweed was hurt during a routine passing drill on Sunday and was taken off the Steelers' indoor practice field on a cart. He later left the team's practice facility on crutches.
"I didn't have direct eyes on him [when he was hurt]. It's just one of those things," Tomlin said.
If the Achilles is ruptured, Sweed likely would miss the season.
Sweed, a second-round draft pick from Texas in 2008, had seven catches in his first two NFL seasons and was a major disappointment to the Steelers. He was removed from the active roster Dec. 22 for what the team said were personal reasons and not the result of an injury.
"There were just some personal things that I went through in my life, but my family and the Steelers helped me get through it," Sweed said Friday. "But I feel like a kid again. It's good to be back playing."