The 11-year veteran said the injury felt much better on Monday.
"Yesterday I couldn't even hold this bag in my hand. Now I can hold the bag in my hand and raise my arm," Brown said. "I'm feeling good about the way things feel today so we'll see what the doctor says."
Still Smith hinted that an MRI reveled Brown suffered some type of tear during his press conference.
"He didn't tear it completely, which is good, but you never know how long it will take," Smith said.
When pressed on the issue, Smith would not elaborate.
Roberto Garza replaced Brown at left guard and got off to a shaky start. He was called for a facemask penalty and also gave up a sack. He improved as the game went on and would be the starter if Brown is forced to miss time.
"He did have a rough start," Smith said of Garza. "The penalty was a big play on Roberto. But he did come back. He played a lot better at the end and that's normally how it goes."
Brown isn't the only member of the offensive line to not be able to finish the game. LT John Tait suffered a sprained left ankle trying to make a tackle during an interception return that was eventually overturned. He downplayed the swollen ankle but he was limping badly.
RB Thomas Jones left with a sprained right knee with just under 10 minutes remaining after rushing for 137 yards on 24 carries. It was his third straight game over 100 yards and fifth in the last six.
His MRI confirmed that the injury is not serious, yet his status for Sunday is uncertain. If Jones is unable to play then Cedric Benson would in line for his first NFL start. The rookie managed just six yards on five carries against the Browns.
PK Doug Brien did not play against Cleveland because of a strained back and said he could barely tie his shoes. Robbie Gould, signed on Saturday as a free agent, connected on his first NFL attempt, a 44-yarder, but later missed from 48.
Smith would prefer not to use two roster spots on kickers and it appears Gould could be the choice over Brien.
"He was our guy this past week and he did well," Smith said. "I'll just kind of take it from there."