The 34-year-old midfielder underwent surgery after having to come off during his Dons debut in a 2-1 season-opening Scottish Premiership victory at home to Kilmarnock.
Robson will miss the trip to Hearts on Saturday and the match against St Johnstone next week but Pittodrie boss McInnes is aiming to have the former Celtic and Middlesbrough player in his squad for the week after the international break.
McInnes told RedTV: "I think there is a good chance he will be back after the international break. It might be touch and go for the Partick Thistle game but he will be there or thereabouts.
"We got the surgeon to go in and have a look and confirm it wasn't anything too sinister, he is walking about freely and will be upping his work next week.
"St Johnstone will be too much of a stretch but we haven't ruled out the Partick game. So I am glad it is nothing too serious."
Veteran keeper Nicky Weaver will replace Jamie Langfield who was sent off in last week's 2-0 home defeat to Celtic after conceding a penalty from which the Hoops took the lead through Kris Commons.
McInnes revealed his confidence in the 34-year-old former Manchester City and Sheffield Wednesday keeper.
He said: "He is a confident individual and there won't be too many surprises for him. He has had a good career and plenty of game experience and I am sure he will relish the opportunity now.
"For goalkeepers, sometimes you have to sit and be patient and always be professional. It is difficult at times but when that opportunity comes, probably more than any other position, you have to go and take it.
"He's not had a lot of games but he has been training well and he will see this as an opportunity and rightly so."
McInnes has consigned to history the Celtic defeat as he looks for three points against the Jambos.
The former St Johnstone and Bristol City boss said: "We have to move on. Even when we win games, it is about moving on to the next game.
"There were some positives (against Celtic), a few things we can learn and things to discuss.
"But this is a different challenge and hopefully one we can meet head on. We are looking to get back on track."