The 26-year-old was handed a three-match ban last month for picking a straight red card against Huddersfield Town following a challenge on Jonathan Hogg.
He served out the last of the three games last weekend when Swansea shared the spoils (1-1) with West Bromwich Albion.
“We are very happy that Jordan can play because he is one of the best attacking players in the Premier League right now," Carvalhal was quoted as saying by Tribalfootball.com.
“He's a very important player to us and he makes a massive difference when he plays. He thinks different than others.
“Jordan is a player with pace and he's a player that keeps the ball very well. He's a player that's very good one-to-one," he said.
“Losing a player like this does make a massive difference. The three games without him, of course, we've missed him. He's hungry to play. He's training very well, training at a very good level in these last four weeks. He's completely ready to play," he added.
Ayew, who boasts of six goals in 30 league appearances, is likely to start for Swansea when they host Everton on Saturday.