Giroud lasted until the 60-minute mark, when he was replaced by Alex Oxlade-Chamberlain, while Arsenal fans were also given a slight scare when Alexis Sanchez was taken off for Danny Welbeck with 11 minutes left.
Wenger says Sanchez's withdrawal was simply a precaution but he confirmed that Giroud has taken a knock, though he would not speculate on the severity of the problem.
"Olivier Giroud did well again and he was important for us. He had an ankle injury after 30-35 minutes and got to 60 minutes," he said, as quoted by BBC Sport.
"I don't know how serious it is. We'll have to assess it. I don't know what the doctors have seen."
Swansea started positively but were undone by some slack defending for Giroud's opener, before two own goals from Jack Cork and Kyle Naughton - both of whom turned Alex Iwobi efforts into the net - ended their resistance and Sanchez added a late fourth.
27 - Arsenal have scored 27 away goals in the Premier League this season, at least five more than any other team. Excursions.— OptaJoe (@OptaJoe) January 14, 2017
"The first half was very intense physically, they gave a lot in the first half and then our pace took over," said Wenger. "They had problems to contain us.
"Swansea were very well organised and they closed down as a unit very well. We lost balls in the first 20-25 minutes which was down to them.
"In the second half, you could see we could create chances. Our transition and accuracy of passing was very good. We were fortunate with the goals, but the chances were there.
"There are many good teams around us and everyone is doing well. We can only focus on our results and hope some go our way."
Swansea midfielder Ki Sung-yueng was booked for simulation after going to ground following contact with Laurent Koscielny towards the end of the first half, when the score remained 1-0 to the visitors.
The South Korea international felt the decision was unjust but urged his team-mates not to allow their heads to drop ahead of a difficult run of fixtures.
"The first half was great even though we conceded a goal - we were still in the game," he said. "Then in the second half we conceded two unlucky goals and you cannot get back into the game against these quality players.
"If you give players space, they have the quality to score. It is hard to concentrate against this sort of players for 90 minutes.
"I think it was a penalty. Laurent Koscielny's leg was on mine but it is the referee's decision. It was disappointing.