The disappointing news is the only blip in an otherwise excellent week for the striker.
After suffering the same scoreline last week to Swansea City, the Hammers showed an immediate improvement with the 23-year-old on the side.
Just one minute was on the clock before Carroll's presence had an impact. His neatly placed header found Ricardo Vaz Te, who set up the influential Kevin Nolan to make the score 1-0.
Carroll continued to terrorise the Fulham defence in the first half.
His fierce aerial duel with Brede Hangeland typified West Ham's entire performance. Sam Allardyce's men worked hard, pressured the opposition into mistakes and played a surprising amount of passes along the floor.
For West Ham fans, the team's ability to mix up their style of play will be a welcome sight. When Matt Jarvis returns from injury, the Upton Park crowd will be sure to see a successful partnership between their two new signings.
Carroll's game was cut short with 20 minutes left. He clashed with Hangeland once more, but this time the impact resulted in a hamstring problem.
Although this injury isn't expected to keep him out for too long, Carroll faces a race against time to be fit for England's qualifying matches.
Roy Hodgson's team will be in Moldova on September 7 before returning to Wembley to play Ukraine on September 11.
Judging based on the striker's recent form, this is a huge blow for England. He performed well at Euro 2012 and scored a superb header against Sweden.
Carroll's display against Fulham demonstrated a player that continues to gain confidence. If he maintains this level of performance throughout the season, Liverpool fans will be wondering why Brendan Rodgers let him go.