He had a dizzy spell before Monday's game and was sent to the hospital as a precaution.
The 45-year-old Wedge will miss at least the next four games as well as a road trip to Boston and Baltimore, but is expected to make a full recovery.
"I've had several conversations with him and the doctors," said Mariners general manager Jack Zduriencik. "We expect a complete recovery. What he needs to do is stay home for the next short period of time. We expect him to be back sooner than later. He sounds normal, talking to him it sounds like everything is fine and he's ready to roll. But we're going to err on the side of caution.
"The common-sense thing is to have Eric rest, and it makes sense that he won't make this trip to the East Coast," Zduriencik said. "When we get back, he'll be evaluated and we'll see where we stand."