While the loss of Holland striker van Persie for at least six weeks with ankle ligament damage is a major blow, Gunners boss Wenger knows it could have been much worse.
Gibbs, meanwhile, looks set to be back in action for the visit of Premier League leaders Chelsea at the end of the month, if not before, with scans showing his foot injury suffered while away with England Under-21s in Lithuania is not serious.
"We knew when Robin came out with this injury that he would be out for a long time, but frankly I feared it would be more because the first news was very, very bad. So it was a relief that he would be out for six weeks," Wenger told Arsenal TV Online.
"Of course it is a disappointment and something we did not want, but I feel we have enough strength to compensate for his absence for a while.
"It will also allow him to be fresh for when he comes back."
On the subject of Gibbs, he added: "Our medical staff called me saying he was in hospital in Lithuania with a suspected broken metatarsal.
"Later on, it was much better news.
"He will still be out for Sunderland, but maybe we could have him back for (the Champions League clash with) Standard Liege on Tuesday."
Nevertheless, Wenger still has selection worries in both defence and attack ahead of the trip to Sunderland, where his depleted side will be out to extend a run of 13 unbeaten matches in all competitions which has seen them climb to second in the league table.
Gibbs had been pencilled in to replace Gael Clichy (back) on the left side of defence, but that role is now likely to be filled by veteran Mikael Silvestre.
Denmark striker Nicklas Bendtner is still sidelined by a groin problem which needed surgery and, with England forward Theo Walcott (knee) short of full match fitness, Croatia marksman Eduardo - who this week agreed a new long-term deal - looks set to take van Persie's place at the head of the Arsenal attack this weekend.
Wenger, though, has been boosted by the availability of midfielder Denilson, the young Brazilian having been out of action since mid-September with a back problem.
Goalkeeper Lukasz Fabianski, Mexican striker Carlos Vela and defender Armand Traore have also all left a busy treatment room during the international break.
However, England Under-21 midfielder Jack Wilshere (ankle) remains unavailable and Abou Diaby, who returned early from the France camp, is still troubled by a calf problem.
Arsenal have displayed a new-found resilience this season which they will need once again at the Stadium of Light, with Steve Bruce's men in eighth place having won four out of six at home.
Silvestre is relishing the challenge.
"They have a good crowd and it is a good test for us," the 32-year-old former Manchester United defender said.
"It is going to be after an international break, so it won't be easy.
"The atmosphere is going to be really hot and hard for us so we have to make sure we don't concede a goal, control the game, and then we will find a way to score."
Silvestre added: "Sunderland are proof that the Premier League is more competitive now. That's why it is one of the most attractive leagues in the world.
"You don't see much of a difference between the teams who are first, second and third in the league and the ones that are 10th, 11th or 12th."