Arda underwent tests at Barca's training ground on Wednesday after suffering the problem while with Turkey during the international break.
Having played in the World Cup qualifying win over Finland, he missed the friendly against Moldova and it was hoped the injury would not be serious.
But he could now miss up to six Barca games at a busy period of the season.
"Medical tests conducted this Wednesday morning have confirmed that first-team player Arda Turan has an injury to the adductor muscle in his right groin," read Barca's statement.
"He is expected to be unavailable for about three weeks."
A three-week timescale means Arda looks certain to miss upcoming LaLiga matches against Granada, title rivals Sevilla, Malaga and Real Sociedad, as well as the first leg of Barca's Champions League quarter-final tie away to Juve on April 11.
The 30-year-old would face a race against time to play the return leg on April 19, with El Clasico against Real Madrid at Santiago Bernabeu to follow that match four days later.