The 23-year-old, who took his maiden first-class five-wicket haul in May, is the one uncapped player in the squad for the games on 16 and 18 June.
"It's been brilliant to play first-team cricket at Durham and to achieve success," said Dubliner McCarthy.
Both matches against Sri Lanka will be staged at Malahide.
John Bracewell, Ireland's head coach, said: "Barry has been in tremendous form with Durham and deserves his opportunity,"
Craig Young (elbow) and Andrew Balbirnie (hip) were not available because of injury.
Meanwhile, Andrew Poynter has announced his retirement from Ireland and inter-provincial duty because of business and family commitments.
Clontarf batsman Poynter, 29, made his Ireland debut against Bangladesh A in 2008 and made 69 appearances for his country.
"I have always found it tough to manage an international and inter-provincial cricket career whilst having to juggle running my own business," said Poynter.
"I'm head of youth coaching at Clontarf CC and have other coaching roles as well as a young family."
Ireland coach John Bracewell said Poynter had made a "tremendous contribution to Irish cricket".
Ireland squad: William Porterfield (Warwickshire, capt), George Dockrell (Leinster Lightning), Ed Joyce (Sussex), Tim Murtagh (Middlesex), Andrew McBrine (North-West Warriors), Barry McCarthy (Durham/Leinster Lightning), Kevin O'Brien (Leinster Lightning/Leicestershire), Niall O'Brien (Leicestershire), Stuart Poynter (Durham), Boyd Rankin (Warwickshire), Paul Stirling (Middlesex), Stuart Thompson (North-West Warriors), Gary Wilson (Surrey).
Durham seam bowler Barry McCarthy's fine start to the season has earned him an Ireland call-up for the one-day series against Sri Lanka.