Old Trafford, known as the "Theatre of Dreams," has been United's home since 1910 and was the stage for some of the most significant moments in the club's history, including their record 13 Premier League titles.
"Wins and losses, successes and failures, highs and lows. We've seen it all. Now, supporters can own a piece of the pitch," United said in a statement on their website on Wednesday.
"Don't worry, there aren't holes in the pitch right now. This is all possible because the Old Trafford pitch was completely dug up and stripped back to its foundation in June, for the first time in 14 years.
"That meticulous project was completed by award-winning groundsperson Tony Sinclair and his team of experts, all to regrow the surface to improve player welfare and water drainage.
"As part of the process, sections of the pitch were carefully preserved and, later, placed into glass cubes to create a special memento for Reds."
The initiative comes at a difficult time on and off the pitch for United.
They finished third in the Premier League last season, but have made a sluggish start to their campaign and sit 12th in the table with just one win from their first five league games.
On Wednesday, the club also reported a seventh straight annual loss, as costs related to player acquisitions and the sacking of former head coach Ruben Amorim this year pushed them deeper into the red.