Areola has taken the No.1 jersey from Lukasz Fabianski this season and has been a standout performer for the Hammers between the sticks, with only Luton Town's Thomas Kaminski (114) making more Premier League saves than the Frenchman (113) to date.
Last weekend, Areola was handed his 27th Premier League start as West Ham let a two-goal lead slip in a chaotic 4-3 defeat at Newcastle United.
However, the 31-year-old was withdrawn at half time in that match with a groin problem having previously been seen in notable discomfort towards the end of the first half at St James' Park.
With West Ham only having three days to prepare for their encounter with Tottenham, Moyes has confirmed that Areola will not recover in time to face Ange Postecoglou's side.
David Moyes issues Alphonse Areola, Nayef Aguerd injury update
Speaking at a press conference on Monday, Moyes said: "Alphonse has hurt his groin. We're hopeful that it's not too serious, but he won't be available on Tuesday night.
"He might be back quite quickly, so we'll just have to see how things develop over the coming days."
The absence of Areola is set to see former Arsenal shot-stopper Fabianski handed a start between the sticks versus Spurs.
Meanwhile, Moyes has revealed that Nayef Aguerd has retuned to training and will be assessed ahead of kickoff after the defender missed the defeat at Newcastle with a shoulder injury.
"Nayef has trained today, so we'll need to see how he is on Tuesday in the lead-up to the game," said the Hammers boss.
"Apart from that, we've just got a couple of knocks here and there, and similarly we'll have to make a call on those tomorrow."
Aguerd has been a first-team regular under Moyes so far this season, starting 20 Premier League games in central defence, but it remains to be seen whether he will be fit to feature from the off against Tottenham.
Kurt Zouma and Konstantinos Mavropanos both started in Aguerd's absence last weekend and could continue at the heart of the defence ahead of the Morocco international; Angelo Ogbonna is another centre-back option at Moyes's disposal.
Elsewhere, West Ham will once again be without the services of defensive midfielder Edson Alvarez, who will serve the second and final match of a two-game suspension.
The absence of the Mexican, who has started 21 of his 25 Premier League appearances so far this season, is set to see Tomas Soucek, James Ward-Prowse and Kalvin Phillips all battle for a place in the first XI on Tuesday.
West Ham currently sit seventh in the top-flight standings, one point ahead of Newcastle in eighth place and four points behind Manchester United in sixth spot.