The 29-year-old finished with 13 disposals and a goal in his Round 1 outing, a 59-point loss to Essendon.
The Hawks confirmed he won't feature this weekend, but expect him to be right for selection in Round 3, per the club's High Performance Manager Peter Burge.
"Chad reported a cramping sensation when he was taking a kick, it was with his calf and the signs were quite minimal," Burge said to club media.
"But given Chad's history medically, it was decided to just take the conservative option and rule him out of the rest of the game.
"He has since had scans and it's a very, very low-grade calf strain. He won't play this week, but I'll expect he'll be running by the end of this week, be back fully training next week and available for Round 3."
While Wingard has been ruled out, the Hawks did confirm that Harry Morrison has been cleared to return from a hamstring injury.
"Harry's hamstring injury is fine, but then during last week he developed some back soreness," Burge said.
"He wasn't able to complete full training on Thursday... it had settled by the weekend, but he hadn't completed main training so we decided to delay his return by a week."
Hawthorn also confirmed that Mitch Lewis, who missed the club's season opening clash after suffering a sprain of his ACL in January, has faced a setback on his return.
"A little bit of fluid (in the other knee) has developed, it's from a previous historical issue in the past," Burge said.
"It's certainly not bad or anything like that, it's just put us in a bit of a holding pattern for the last week, so we've delayed his return timeframe by a week to allow us a little bit more time to make sure we get a good result."