Balshaw has not recovered sufficiently from the injury he suffered three weeks ago, when he tore his right quad.
Although good progress has been made, it will be another three to four weeks before he will be back in training.
A delighted Cueto was informed of the decision on Tuesday morning and is now making plans to join the Lions in Wales.
The Sale Sharks winger said: "This is brilliant news, although it came as bit of a shock. I was training when (Sale director of rugby) Philippe Saint-Andre came over and passed on the message that I'd been selected.
"It's fantastic and the season couldn't have gone any better for me. I'll still be playing for Sale in the Challenge Cup final on Saturday."
Lions head coach Sir Clive Woodward said: "Obviously everyone is extremely disappointed for Iain.
"He is a terrific player and would have been a great asset to the tour.
"But obviously I am delighted that we have someone of the calibre of Mark Cueto to call upon.
"And it is good that he can join us as we begin to prepare for the challenge ahead."
Balshaw added: "I was given the best opportunity to try and get right and it was not to be but that is the nature of sport. I wish Mark good luck for the tour."