McLaren did not say who would stand in for Alonso for the Monaco race, one of the highlights of the Grand Prix calendar - but news of his absence sparked speculation that his position could be filled in Monte Carlo by Jenson Button, another ex-Formula One world champion, who remains under contract in an ambassadorial role with McLaren.
Alonso will race a Honda-powered Andretti car branded as a McLaren for the Indianapolis 500, one of US motorsport's most prestigious races.
The 2005 and 2006 F1 champion said he wanted to compete at the Brickyard to have a chance of fulfilling a career ambition of completing motorsport "Triple Crown" in winning the Monaco Grand Prix, the Indianapolis 500 and the Le Mans 24 Hours.
The only driver to achieve the feat was the late Graham Hill, also a double F1 title-holder.
"I realise I'll be on a steep learning curve," said Alonso, "but I'll be flying to Indianapolis from Barcelona immediately after the Spanish Grand Prix.
"I've won the Monaco Grand Prix twice, and it's one of my ambitions to win the Triple Crown. It's a tough challenge, but I'm up for it.
"I don't know when I'm going to race at Le Mans, but one day I intend to. I'm only 35 and I've got plenty of time for that."
Alonso is now in the final year of what has been a frustrating three-season deal with McLaren, with his failure to finish last week's Chinese Grand Prix in Shanghai the latest disappointing result.
He joined in the hope of winning a third world title, after two triumphs with Renault, but his best results have been three fifth places, with much of the blame attributed to the poor performance of the Honda engine.
However, Alonso insisted Monaco would be the only F1 race he would miss intentionally this season.
"Monaco will be the only 2017 Grand Prix I'll be missing," he said. "I'll be back in the McLaren for the Canadian Grand Prix in Montreal in June."
The Andretti team won at Indianapolis in 2015, with rookie driver Alexander Rossi the surprise winner at the 100th running of the Indianapolis 500.
Andretti chief Michael Andretti, a former IndyCar champion who raced in F1 for McLaren, said Alonso was capable of repeating Rossi's achievement.
"Fernando’s lack of experience on super-speedways is not of concern to me," he said. "Indianapolis is one of the best places for an IndyCar rookie to start because there's the opportunity for so much practice time on the track - and, as we have demonstrated, it can be won by a rookie," added the son of three-times IndyCar champion and 1978 F1 champion Mario Andretti.
Meanwhile McLaren boss Zak Brown, who will also be in Indianapolis instead of Monaco, said: "Could Fernando win this year's Indy 500? Well, I wouldn't be so silly as to make any such rash prediction, but I expect him to be in the mix."
"Put it this way, the team he'll be racing for won the race last year, using the same Honda engine, and he's the best racing driver in the world. That's quite a compelling combination."
McLaren won the Indianapolis 500 with its own car in 1974 and 1976, but IndyCar is now a 'spec' formula where all teams use the same basic car, although different manufacturers are allowed to design their own aerodynamic bodykits.