"As we just told Morgan, it's not our intention to send him to the Minor Leagues at this stage," Astros general manager Tim Purpura said. "It's not an option I think for him or us. So we'll try to see if we can make a trade for him and give him another opportunity elsewhere."
Ensberg, a ninth-round draft choice in 1998, had spent his entire career in the Houston organization.
"These are tough ones, a guy comes through your organization, played in the World Series for you, been a big part of your club for a long time, but we feel like this is a move that's going to make our club better and obviously with the acquisition of [Ty] Wigginton, Morgan becomes the odd man out," Purpura said.
Houston acquired Wigginton from Tampa Bay on Saturday for right-handed reliever Dan Wheeler. The Astros summoned Mark McLemore on Sunday to take Wheeler's spot in the bullpen.
Wigginton, who will wear No. 21, was in the lineup batting fifth for Sunday's game against San Diego.
Jim Molony is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.