The 25-year-old was not breathing and had sunk after completing her routine in the solo free final in Budapest.
Her coach, Andrea Fuentes, pulled Alvarez to the surface before she was taken away on a stretcher.
The US swim team later released a statement from Fuentes saying Alvarez "feels good now".
Alvarez previously fainted following a routine during an Olympic qualifier in Barcelona last year, with Fuentes also rescuing her on that occasion.
Of the more recent incident, Fuentes said: "Anita is okay - the doctors checked all vitals and everything is normal - [her] heart rate, oxygen, sugar levels, blood pressure, et cetera… all is OK.
"We sometimes forget that this happens in other high-endurance sports [such as] marathon, cycling, cross country. We all have seen images where some athletes don't make it to the finish line and others help them to get there.
"Our sport is no different than others, just in a pool, we push through limits and sometimes we find them.
"Anita feels good now and the doctors also say she is okay. Tomorrow she will rest all day and will decide with the doctor if she can swim free team finals or not."
Spanish newspaper Marca reported four-time Olympic medallist Fuentes as saying she had jumped in "because the lifeguards weren't doing it".
And speaking to Spanish radio, she said: "It felt like a whole hour. I said things weren't right, I was shouting at the lifeguards to get into the water, but they didn't catch what I said or they didn't understand.
"She wasn't breathing. I went as quickly as I could, as if it were an Olympic final."
Alvarez scored 87.6333 points for her routine, finishing seventh in the final.
(BBC News / Pics - Dailymail)