The 29-year-old has eight goals this season in 1,455 Premier League minutes, including four in his last seven outings.
Chelsea FC took the lead in the 36th minute at Stamford Bridge thanks to Cesar Azpilicueta's close-range finish.
He'll be a big miss against Chelsea, although it's a game that West Ham will be hoping to get something out of, as opposed to expecting.More news: Gun Store Employee Says YouTube Shooter Did Not Stand Out
But the fact remains, Conte has presided over just three wins in Chelsea's last 10 Premier League games.
Morata failed to test Hart with a towering header that soared over the target on 55 minutes, while Moses curled a left-footed shot narrowly wide of the left post 14 minutes later after Masuaku lost possession inside his box.
West Ham, who had been much improved in beating Southampton 3-0 a week ago, offered little until Hernandez's intervention soon after coming on.
ExWHUemployee, a solid source of West Ham news, reported that the player would not make the game on Sunday. That said, their form has been so erratic over the past couple of months that in likelihood, they will welcome Liverpool to Stamford Bridge next month with the top four already beyond them.More news: Polls close in key Hungarian parliamentary election
The half ended with the home side leading by a single goal.
His performance in front of goal today was also less than inspiring, as he frequently mistimed his runs, and even had a goal disallowed due to his inability to keep on track with West Ham's back line.
On the hour mark Morata had a goal disallowed for the second time, once again he was denied because he was in an off-sides position.
Chelsea midfielders Willian and Eden Hazard were the game's most creative forces and were both involved in the few scoring opportunities before their team finally struck.More news: US, China step up trade war