Everton's Barry will be fit to face Swansea
The midfielder suffered a leg injury following a tackle from Kevin Theophile-Catherine during Everton's 2-1 win over Cardiff City on Saturday, although he was able to finish the game.
Martinez revealed that the 33-year-old had stud marks on his leg and was lucky to escape serious injury.
"We've been very fortunate," a relieved Martinez told the club's official website. "It was a strong knock but he was caught in a position that has allowed him to recover quickly.
"It was painful and he has got stud marks but it didn't affect any joints. The ankle and the knee are in perfect condition so luckily enough on this occasion Gareth is fine and today (Tuesday) he will train as normal."
Martinez also confirmed that on-loan striker Lacina Traore's rehabilitation from a hamstring injury is going well and he could make a first-team return soon.
"He is progressing really well," the Spaniard added. "He has had the first part of the treatment and his recovery is quicker than we expected, so we are very pleased.
"His attitude has been very much focused on coming back and playing before the season ends, which we are very much looking forward to.
"The signs are very good that we will see Lacina in an Everton shirt before the season ends."