Morneau, who is 1 for 10 in the series against Kansas City and 3 for 20 on this trip has a sore left wrist. Span was a late scratch with a stiff neck.
Span hurt his neck in a plate collision Friday night with Royals catcher Brayan Pena as he was out in a foiled attempt to score on an inside-the-park home run.
"Morneau is beat up," Twins manager Ron Gardenhire said. "He came to me today and said he needed time. He's been playing with it and playing with it and playing with it and now it's time. He's needs a blow. Today, he's a 'no.' We'll see about tomorrow.
In the revised Twins lineup, Ben Revere switched from right field to center and batted leadoff for the first time. Span, who had played in 55 of the Twins first 56 games, is hitting .300 and leads the team with 32 runs.
Jason Repko, who was not in the original lineup, made his ninth start of the season, playing right. Brian Dinkelman started in left, making his big league debut.
The Twins have eight players on the disabled, but it appears likely left-hander Francisco Liriano will be activated Tuesday and start at Cleveland. Liriano, who has been out with shoulder inflammation, threw a bullpen session Saturday at Kansas City.
"He felt good," assistant trainer Dave Pruemer said. "He's on track for Tuesday."
Catcher Joe Mauer, who has played only nine games this season and is on the 60-day disabled list with bilateral leg weakness, is rehabbing with Class-A Fort Myers in the Florida State League and was scheduled to be the designated hitter Saturday night.