The move was announced before the game in Chicago on Saturday.
Harden is 4-2 with a 4.74 ERA. He has not pitched since May 17 because of a midback strain. He went on the DL five days later, when Carlos Zambrano was activated.
Acquired in a trade with Oakland last season, Harden is 45-22 with a 3.33 ERA for his career.
Sending down Scales, who was batting .241 since his major league debut early last month, leaves the Cubs short a utility player. They decided to keep 13 pitchers for now after playing five extra-inning games this month, including a 2-1 loss to Houston in 13 innings Thursday.
Meanwhile, the Twins held outfielder Michael Cuddyer out of the lineup because of an inflamed right index finger.
Cuddyer, who sprained a ligament in the finger on May 31 in Tampa Bay, missed four games but had played in the Twins' past seven before aggravating the condition Friday night. He is batting .262 with nine homers and 34 RBIs.
"His finger blew up on him last night during the middle of the night," Minnesota manager Ron Gardenhire said. "I know when he walked in this morning it was ugly. He said if he would have had a saw, he would have cut his hand off last night."
Cuddyer was examined Saturday by a doctor, who said the inflammation could be result of some blood coming free from the original injury. Cuddyer said he was frustrated by the mystery surrounding this latest setback and hopes to get a more definitive answer when he sees a hand specialist on Monday.
Information from The Associated Press contributed to this report.