Williams lasted only 17 minutes in the game before being forced off after stretching for the ball.
"He's gone to the hospital to get an X-ray," said Giggs.
"He's gone to check that there's no real damage, maybe just a cracked rib.
"They're really painful. You breathe, you sneeze, you cough - it's agony. Fingers crossed he'll be okay because we want him fit and back for pre-season."
Speaking about the game itself, Giggs was in a positive mood as Wales fought for a draw.
"It's a clean sheet against a very good team," Giggs added. "There were also 80,000 Mexicans making it difficult for us, so I take that.
"The next part now is to show our quality, because we can do better in the final third.
"We were not rewarding the way that we were defending and the way that we had worked. So that's the next step."