England first folded Sri Lanka for 185 and chased down the target inside 35 overs.
The 56-year-old is asymptomatic and will now isolate himself for 10 days.
Yorkshire batsman Dawid Malan has been added to the squad for the forthcoming one-day international series.
In the end, Jos Buttler along with Jonny Bairstow guided England over the line by eight wickets in hand and 17 balls to spare.
England all-rounder Chris Woakes' last international cap in T20 format came in November 2015 against Pakistan.