The striker pulled a muscle in Sunday's 1-0 defeat by Birmingham, withdrew from the Republic of Ireland squad to face Wales on Tuesday and has not trained all week.
Keane, thought to be on ?65,000 a week, is on loan from Tottenham Hotspur until the end of the season and scored on his West Ham debut in the 3-1 win at Blackpool on February 2.
Shot down: Keane pulled a muscle against Birmingham
But two matches in five days proved too much for the 30-year-old, who had started just four games for Tottenham this season prior to joining the Hammers.
Keane's injury is a massive blow for West Ham, who are bottom of the Premier League with just 12 games left.
Great Scott: Grant says Parker will build on his eye-catching display in England's win over Denmark
Avram Grant's side travel to fellow strugglers West Bromwich Albion tomorrow, a side against whom Keane has scored nine goals in 15 games.
Grant will judge after training today whether new signing Demba Ba is fit enough to start at The Hawthorns but the game will come too soon for Thomas Hitzlsperger, who has still to make his senior debut for West Ham.
The German midfielder played 63 minutes in a 4-1 win against West Bromwich's reserves this week after six months out with a thigh injury.
Grant said: 'He (Hitzlsperger) was maybe our best player in the training camp before the season started. He gave us something that we needed this season - a lot of intelligence in the game - and he is a hard worker.
'He was good for us but he unfortunately got injured - one of many this season - and I hope he will come back to the same form.'
The West Ham manager also backed midfielder Scott Parker to build on his impressive second-half display for England against Denmark on Wednesday.
Grant said: 'He deserved to be there and he played well. It's good for him and good for England. 'He is 30 but his body is in very good condition. He has a contract for another five years here.
'He can come from the bench, he can start, he could give a lot of things that can help the national team. 'I think he is (one of) the youngest in the midfield. So he is in the youth team.'
?Reid backs boss Grant to rescue Hammers from threat of relegation Scotland v Brazil at Arsenal? Prestige friendly could take place in MarchKeane set to miss Ireland's clash with Wales after picking up calf injuryWest Ham United FC news from across the web ?Explore more:People: Robbie Keane, Thomas Hitzlsperger Places: Birmingham, United Kingdom, Republic of Ireland, Wales, Denmark
Source: Daily Mail
Source: Daily Mail