The shock news has created a buzz in the motor racing world, but many fellow drivers said they would never skip a grand prix, while team bosses revealed they would not allow their own racers to do the same.
“I think he needs to see a psychiatrist personally,” said Red Bull boss Christian Horner.
“Would we let our drivers do it? No.”
Alonso said in Bahrain that his former boss Ron Dennis would not have allowed it either, and former F1 supremo Bernie Ecclestone agreed.
“I think it’s probably good for Alonso but if I could have persuaded McLaren not to go I would have done it,” said the 86-year-old in Bahrain.
“I would have said ‘Wait until your contract finishes and then do what you like — but you are in the middle of formula one.”
But there is not only criticism.
1997 world champion Jacques Villeneuve hailed Alonso’s bravery for taking on the challenge of a race he himself won in 1995.
“Fernando has this,” said the Canadian, using his hands to symbolise ‘balls’.
“I don’t understand when it’s said that the risks are too high,” Villeneuve told Brazil’s Globo in Bahrain. “Yes, but if you’re a driver and so many other drivers are doing it, you cannot be afraid.
“Are you a driver or not?” he added.
Indeed, Villeneuve said it is the danger of Indianapolis that means the quality of the field is high.
“Why are most of the drivers in the Indy 500 not paying drivers?” he asked rhetorically. “Because daddy is not going to give you money to race somewhere you can get hurt.
“But what are the risks today in F1? Hardly anything. And what happens? It’s full of paying drivers.”
When asked about the criticism of his and McLaren’s Indy 500 decision, Spaniard Alonso said in Bahrain that he expected it.
“We spoke before the announcement that the drivers would say they would never miss a grand prix, and the bosses would say they would never let their drivers go to the Indy 500,” Alonso told the Spanish broadcaster Movistar.
“We said this reaction (in F1) would be normal because this weekend the media coverage is high because of Indy, the sponsors want to go, the TV wants to go, journalists want to go — so I think it’s normal,” he added.