Morrison was removed from Monday's opener of the four-game set in the first inning due to the injury, with infielder Nick Franklin recalled from Triple-A Tacoma to fill the available roster spot.
The 26-year-old Morrison, obtained in a trade with Miami over the winter, had gotten off to a horrendous start to the season, recording only three singles in 20 at-bats over eight games.
Franklin spent much of last season as Seattle's regular second baseman, but opened 2014 in the minors following the club's acquisition of All-Star Robinson Cano. The 23-year-old was hitting well for Tacoma, going 17-for-43 (.395) with four home runs and 13 RBI in 11 games.
In 102 games as a rookie last year, Franklin hit .225 with 12 homers, 45 RBI and six stolen bases.