American Howard was replaced at halftime during the game against Stoke City on Boxing Day and missed the defeat by Newcastle United on Sunday.
"Tim will be out for between five and six weeks," Martinez told reporters.
"It is an injury to his left calf. As a goalkeeper it's really unusual to get an injury by kicking a ball."
Spaniard Joel Robles is the 35-year-old Howard's deputy.
"I thought Joel was very calm against Stoke and did well against Newcastle, but we will assess whether we need cover," added Martinez.
Everton lie 12th in the table after an indifferent first half of the season.
(Reporting by Ed Osmond. editing by Patrick Johnston)
Share
