It will be Wilson's first outing in a Ford Fiesta RS WRC since finishing eighth on last year's Rally GB. Wilson has competed in Sweden five times before.
Team boss Malcolm Wilson said: "Unfortunately Nasser is ill and can't travel. The team called last night and said they would like Matthew to drive the car if he was free and he was."
Wilson flew out to Sweden earlier and was expected to test the car for an hour on Monday night before starting his first recce with Al-Attiyah's co-driver Giovanni Bernacchini, who cannot be changed, on Tuesday.
"After so much disappointment last season, it is an absolutely fantastic feeling to know that I will be back behind the wheel of a World Rally Car this week," said Wilson, who missed Sweden with a broken ankle last year and later lost his M-Sport seat due to a sponsorship issue.
"It all came as a bit of a shock really - I found out I would be competing last night and flew to Sweden this morning!
"I need to say a big thank you to Nasser for this opportunity, and the entire team wish him a speedy recovery."
The Cumbrian is sure working with Bernacchini - who reads Al-Attiyah's notes in English - will be no problem.
"I'm confident that Gio and I will work well together," said Wilson. "It's always tricky adapting to a new co-driver, but he is one of the best in the business."