The former Wigan manager, who succeeded David Moyes at Goodison Park in June, will take his side to Carrow Road when the new season starts on 17 August.
West Brom will be Martinez's first home opponents, and the third fixture will see Everton travel to south Wales to take on newly-promoted Cardiff City.
Martinez's first Merseyside derby will be on home soil when Liverpool make the short trip across Stanley Park on 23 November, with the return fixture at Anfield on 28 January.
Everton will take on Premier League champions Manchester United and their former boss Moyes at Old Trafford on 3 December, at the start of a busy month which sees a trip to Arsenal four days later.
They are at home to Sunderland on Boxing Day with Southampton visiting Goodison Park on 28 December.
Moyes will return to his old club when Manchester United visit Everton on 19 April.
Everton's season concludes when they face promoted Hull City away on 11 May.