Glover, a 15-year NFL veteran who returned to the lineup this season after having back surgery in December, will be hospitalized for four or five days.
"It's my understanding it's not life threatening," coach Mike Holmgren said Wednesday. "But that does not diminish the seriousness of it."
Glover, 36, had trouble breathing during Sunday's game against Buffalo in the Kingdome, but thought it was a reoccurence of asthma problems he had as a youngster.
Doctors discovered the blood clot when he underwent tests Tuesday night.
He's being given blood thinners in the hospital to dissolve the clot, Holmgren said.
Holmgren said Glover will probably be placed on injured reserve and replaced by Chris Gray for Monday night's game at Green Bay.
Gray, a seven-year veteran in his second season in Seattle, took Glover's place last season after eight games. Glover, who had been injured during a practice, eventually was diagnosed with a fractured disc in his back.
"It's tough," said Holmgren, whose team is 4-2 and in a three-way tie for first in the AFC West. "He's one of our leaders and he's a good player. The center gets overlooked at times, but it's really a crucial position for you."
Holmgren said doctors weren't sure what caused the blood clot.
Holmgren said the doctors did tell him the clot shouldn't be career-ending.
"There will be three to six months of treatment and watching this, and then after that it's my understanding he can play," Holmgren said.
Glover started all six of the Seahawks' games this season, giving him 175 starts in 191 games.
He came to Seattle as a free agent last year after 13 seasons in Detroit, where he was a three-time Pro Bowl selection. The Lions made him a second-round draft choice out of Maryland in 1985.
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