The 20-year-old was injured in training and played no part in yesterday's 2-2 draw at Leicester City.
Martinez said he was hoping for the best, but feared that the midfielder may miss a significant part of Everton's season and several of England's Euro 2016 qualifiers.
"We had a scan, but it was difficult to determine the extent of the injury. It is a problem with a medial ligament in his knee, but we don't know how bad the injury is," he said.
"We know there is a partial tear of the ligament and that could mean anything from seven weeks to four or five months, so we need to be cautious."
"I think Ross Barkley is a phenomenal footballer and we are going to miss him - there are no two ways about it," Martinez said. "The squad should be big enough and be able to cope with losing a player, but it is disappointing."
Everton's neighbours Liverpool continue to spend the money generated from Luis Suarez's transfer to Barcelona, by making the Sevilla left-back Alberto Moreno their eighth summer signing.
Moreno completed formalities at the club's Melwood training ground yesterday although he was not registered in time to feature against Southampton today.
Moreno has been a target for some time and was pulled from Sevilla's UEFA Super Cup match against Real Madrid at the Cardiff City Stadium last week when the extent of Rodgers' interest became apparent.
The 22-year-old came through the ranks at Sevilla. He was in tears waving farewell to their fans at the final whistle.
He said: "I spoke with Xabi Alonso, Pepe Reina and Alvaro Arbeloa and they told me [Liverpool] is a spectacular club. They all told me I can grow a lot here as a footballer as this is a massive club."