Moriarty, who played in the tour opener against the New Zealand Provincial Barbarians, becomes the Lions' second loss to injury after fullback Stuart Hogg departed with a facial fracture.
"We are really disappointed for Ross," said Gatland, adding: "It is disappointing to see injury cut his Tour short but we wish him all the best with his recovery."
Moriarty's departure was announced shortly after Gatland called up Wales's Cory Hill, Kristian Dacey, Gareth Davies and Tomas Francis, and indicated more reinforcements would follow.
All four new arrivals played in Wales's victory over Tonga in Auckland on Friday, while Scotland are in Australia and Ireland are touring Japan.
England coach Eddie Jones, who is leading his team on a tour of Argentina, earlier urged Gatland to choose reinforcements on "merit rather than geographical proximity".
But Gatland said: "Bringing in these players from an identical time zone, who can hit the ground running and step straight in rather than having to adjust following long-haul travel will help us manage players before the first Test (and) give us quality training numbers to prepare properly."
The Lions, who play the Maori All Blacks in Rotorua on Saturday, said they would make another announcement about reinforcements after this weekend's Tests.
Gatland arrived with an original squad of 41. As of Saturday, the Lions are playing three tour games plus three Tests over the next three weeks.
"We have said all along that we need to give ourselves the best chance of winning the Test series and that could potentially involve calling up players," Gatland said.
Earlier Jones told the BBC: "The Lions is a prestigious team -- when you become a Lion, you're remembered for life.
"My only comment would be I would like to see it picked on merit rather than geographical proximity."
He added: "It's only a 13-hour trip from here to New Zealand."