The girls ate othalanga, a local fruit, at the Water Sports Centre in southern Kerala state, reports said.
The girls, all rowers, were allegedly being harassed by senior athletes and their trainer, their families allege.
The government-run Sports Authority of India which runs the centre has ordered an inquiry into the incident.
"They had left behind a suicide note. The jurisdictional magistrate has also recorded the statement of one of them. The police investigation is also on," SAI (Sports Authority of India) director general Injeti Srinivas told reporters in Delhi.
SAI official G Kishore, who has been asked to conduct the inquiry, told BBC Hindi's Imran Qureshi that the condition of one of the girls admitted to hospital was critical while the other two were out of danger.
The athletes were taken to hospital on Wednesday evening after they were found unconscious in a room of their hostel.

The Irishman, who turns 21 on Saturday, will remain at Craven Cottage until the summer of 2018.
Kavanagh, who can also play at left-back, has made a total of 11 appearances since his debut for the west London club last August.
He scored his first goal for the Whites in the 1-0 win at home to Norwich City in October.

Gloucestershire reached 253-6 with four balls to spare after Cockbain shared a stand of 172 with Benny Howell (81).
Lukas Carey was Glamorgan's best bowler with four for 38.
Glamorgan made 252-9 thanks to openers Jacques Rudolph (60) and David Lloyd (49). But Glamorgan lost seamer Ruaidhri Smith to a leg injury suffered while bowling only his second over.
Both teams now play their opening first-class friendlies against student opposition, starting on Tuesday 28 March. Glamorgan host Cardiff MCCU while Gloucestershire face Durham MCCU in Bristol.
A 15-year-old Indian athlete has died and three others are in hospital after allegedly consuming poisonous fruit in what is suspected to be a suicide pact.
[NEXT_CONCEPT]
Fulham midfielder Sean Kavanagh has signed a new contract with the Championship club.
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Gloucestershire beat Glamorgan by four wickets in their pre-season friendly thanks to Ian Cockbain's 125 not out.