The Netherlands striker returns to the Emirates Stadium for the first time since he joined the Red Devils for £24 million last summer.
United captured their 20th Premier League title on Monday and Arsenal will give the newly-crowned champions a guard of honour, but the manager doesn't see Van Persie's return as anything other than a normal fixture.
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"There was some booing of him at Old Trafford [in the corresponding fixture] but that's modern society.
"Robin showed in his celebrations how much winning the league meant to him."
Arsenal are fighting hard for a Champions League spot and could do with a good result on Sunday, but Sir Alex has warned the Gunners he will still be playing his best XI despite having already wrapped up the title.
“We have a few bumps and bruises from the other night but it is hopefully nothing serious and I expect to have a strong side on Sunday,” he added.
“Having won the league, there's always a danger of falling into the trap of 'it's all over and we can relax' and enjoy ourselves but I think we've got a duty to other clubs who are chasing Champions League places.
“Also, the rivalry we've had with Arsenal and then Chelsea over the years does put an edge to these games anyway so hopefully we'll represent ourselves in the right way.”