Assistant Manager Davie Irons will remain in charge of Gretna until the end of the season.
Irons will deputise for Alexander until the end of the season
Manager Rowan Alexander has been given leave of absence by the club to recover from an unspecified illness.
Irons took control of the First Division club for the games against Dundee and Livingston.
He will now see out the remaining six matches with the help of first-team coach Derek Collins, as Gretna look to clinch promotion to the SPL.
Alexander may return to the club before the end of the season to take on light duties that will assist his recuperation.
Director Graeme Muir told BBC Scotland: "We respect what Rowan has achieved in recent times, but now he needs time and space to recover from this illness.
"He's seeking advice and that's a good thing. All members of staff have been informed and are supportive."
Alexander has been in charge at Gretna since 2000 and was at the helm when the club secured their place among the ranks of senior Scottish clubs in 2002.
Since then he has won the Division Three and Two titles, as well as steering the club to the Scottish Cup final last season and a place in the Uefa Cup.
Gretna are seven points clear at the top of Division One with six games to go as they aim for a third successive promotion.