1-0 victory on Saturday that moved them up to third in the Premier League ahead of Chelsea's visit to Liverpool.
Arteta, Arsenal's captain on the day, played on for the rest of the match, but Wenger fears the midfielder could yet suffer a reaction ahead of next weekend's meeting with Manchester United.
"We will see if he is fine. He played the second half. I don't know how much damage is done. It is a kick, a bad kick," the Arsenal manager said.
"I don't know if he has twisted his ankle or not. In these kind of things, it is a question of a fraction of a second.
"You can just ease a little bit off. If you are fully on your foot at the moment you get it, you break your leg. If you ease a bit off, maybe that is why he got away with it."
Wenger had no doubt Sidwell's challenge would receive a red card, but he did have some sympathy with his striker Olivier Giroud, who was sent off in the 90th minute for a similar challenge.
The manager will make a decision on whether to appeal against the decision -- which will rule Giroud out of three of Arsenal's final four games -- after reviewing footage of the incident.
But he said: "I spoke to Giroud and he said to me he slipped at the moment he went for the ball. It is confirmed by the television.
"I haven't seen the replay. He is not a tackler. He went a bit over the ball and knowing Sidwell had been sent off before, I had no illusion about the colour of the card."
Arsenal's win shifted the pressure onto Chelsea and Tottenham Hotspur in the battle to fill the final two Champions League places.
Wenger said: "We are on a strong run, we go into the next game and focus on winning that. The next game we know will be Manchester United, so it is a good challenge for us. But it is important for us to win our games, of course."
Wenger started with Jack Wilshere on the bench after recently admitting he may have rushed the England midfielder back from injury too quickly.
"He played last Saturday and Tuesday. He is still not completely recovered, and pain-free. I took the decision to rest him today," said the Frenchman.
Fulham were unfortunate to lose to Per Mertesacker's 43rd-minute goal, when the home side were exposed at a free-kick.
"We did ever so well since December on set plays, but we had a spare man in Brede (Hangeland) and now to concede against Chelsea and Arsenal in the same way, it's disappointing," said Fulham manager Martin Jol.
Eyon Enoh impressed again for Fulham but Jol admits he has not yet decided whether or not to take up the option to buy the on-loan Ajax midfielder.
"Yes, we have an option to buy, but there are still a few things to think about," Jol said.
"We have one or two options as well. It's one for the end of the season."
Jol voiced his frustration at Sidwell's tackle, particularly as the player was making his return following a three-game suspension for a sending off against Queens Park Rangers.
"I was annoyed with him, but he says it is not intentional," said the Dutchman. "Sometimes you see tackles and you think, 'Yeah, OK, it's a decision.'
"It was probably a red card, but sometimes you have to take these decisions in the spirit of the game so as his manager, I would not have given it."