The 32-year-old damaged his shoulder during his team’s opening tour match against Essex last week.
“We’re hoping that we can get him bowling again pretty soon,” head coach Graham Ford said.
Prasad, 32, took five wickets in the second innings against England at Headingley two years ago to help Sri Lanka clinch the series.
“We’ll have to build him up and get him bowling a number of overs in the nets to have him prepared potentially for the second or third test,” Ford said.
Prasad has taken 75 wickets in 25 tests. (Courtesy Reuters)