The on-loan winger's parent club released a statement on Thursday claiming the 19-year-old could be out for "six to eight weeks".
News of Deulofeu's injury causes a midfield dilemma for Martinez, with Arouna Kone and Darron Gibson already ruled out for the remainder of the campaign.
The Spaniard is now forced to look for temporary replacements when the transfer window opens in January, with fears another spate of injuries could derail his side's top-four ambitions.
Speaking to the Liverpool Echo, Martinez said: "I do feel that Arouna Kone and Darron Gibson are two players who were going to have big roles for us.
"So I will look if there are any options to bring in anyone in January, just to have that peace of mind and make the squad a little bit stronger.
"It could be the loan market. It is a short-term situation the one we are in, because I'd love to see Darron and Arouna back on the pitch. A short-term solution would help in that respect.
"But overall, I've been delighted with the way the lads have adapted."
Despite the midfield concerns, Everton striker Romelu Lukaku is thriving with eight goals to his name already, while Martinez is confident Nikica Jelavic and Steven Naismith can also provide more than ample cover.
"I've been able to work internally now and we have three strikers in Romelu, Jela and Steven Naismith, who has been playing in that role for Scotland and has done really well," he added.
"I've seen him play that role for Scotland and Rangers too, so in that respect I'm happy with my options.
"I don't want to lose any of those players. If we did, we'd be a little weak in that position. But I'm pleased with the strength we've got everywhere else."