The Sweden international was stretchered off at Upton Park in a first-half clash with Steven Taylor.
Alan Curbishley:: "I think Taylor has tried to leapfrog him and landed on him. He has been raked all down the side and front of his face and cracked a rib.
"That's another one out for us but we are hoping he will be okay for the Euros.
"We were playing ever so well for 40 minutes and could perhaps be even more in the lead. We just had a crazy couple of minutes.
"It was a terrific ball - the type that Martins feeds on - and Tomkins just got caught under it but that's another learning curve for him.
"That turned the game in their favour. But I'm delighted with the way we played, for the whole game really, but obviously two wasn't enough."