The International Cricket Council said the 29-year-old is "required to undergo testing within 14 days".
Eranga, who has taken 53 wickets at an average of 37.47 in 18 Tests, can bowl until the results are known.
He had match figures of 0-104 as England won by nine wickets to take a 2-0 lead in the three-Test series.
The final match at Lord's starts on 9 June.
Sri Lanka seamer Shaminda Eranga was reported for a suspect bowling action in the second-Test defeat by England at Chester-le-Street.