Clare has made 20 appearances for the Silkmen so far this season, scoring eight goals.
His last start for the club came in a 1-1 draw at Colne at the beginning of December.
The latest series of Love Island, which will see contestants search for love in a South African villa, will begin later this month.
A club statement read: “Tom approached us with the request a number of weeks ago and we were happy to show the same loyalty that he has to us since becoming one of our first ever signings back in 2021.
“Despite the fact that we are disappointed to lose a player of Tom’s calibre for the foreseeable future, we also recognise the incredible opportunity that this represents for both him and his family on a personal level.
“Tom remains very much part of our plans here at the Leasing.com Stadium and has expressed his unwavering desire to return to the club after the show.
"We wish Tom every success and look forward to welcoming him back to the club in due course."
Neil Danns’ side are next in action away at Kidsgrove Athletic on Saturday.
Photo credit: Macclesfield
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