The Italian international has forged an impressive partnership with fellow Hammers centre-back Winston Reid since signing from Serie A champions Juventus in the summer.
But the east Londoners will have to make do without Ogbonna's imposing presence after the club's official website confirmed the injury he picked up just before half-time in the 2-0 win over Newcastle United on Monday will keep him out for the next three weeks.
'The injury is not too bad'
"We will start with an update on the condition of Angelo Ogbonna, who suffered a hamstring injury in the Barclays Premier League victory over Newcastle United on Monday evening," Vandenbroucke told whufc.com.
"Angelo underwent a scan on his injured left leg on Wednesday and we have received the results.
"The injury is not too bad and we hope he will be back in action within three weeks."
The news was later confirmed by West Ham co-owner David Gold on social networking site Twitter.
Angelo Ogbonna will miss at least three games with a injured hamstring. dg— David Gold (@davidgold) September 16, 2015
Crucial period could shape Hammers' season
While the news could have been a lot worse, it does mean Ogbonna will sit out a clutch of four games which could shape West Ham's season.
Saturday sees Slaven Bilic's side make the tough trip to Premier League leaders Manchester City, before taking in a Capital One Cup tie at Leicester City next Tuesday night.
That is followed by a home match against Norwich City and the long trip up to Sunderland the week after.
Should Ogbonna sit out the full three weeks and miss those games, he will not have the chance play again until mid-October, as there is another international break. The east Londoners are then back in action at Crystal Palace on October 17.
The Hammers will be aiming for a minimum of four points from those matches and progression to the next round of the cup.
A chance for Tomkins or Collins
Ogbonna's injury will give either James Tomkins or James Collins the chance to impress Bilic alongside Reid at the heart of the West Ham defence.
Tomkins seems the more likely to replace him, given he switched to centre back to cover for Ogbonna after starting at right-back in the win over the Magpies.
As a knock-on effect Carl Jenkinson, on loan from Arsenal, could win back his place at right-back if Tomkins does move back into central defence from the start at the Etihad.