Gutierrez was placed on the DL on April 11 with a left hamstring strain and played two rehab games at Class A Advanced Rancho Cucamonga.
Van Slyke, used primarily against left-handed pitching, hit .129 in 21 games. He hasn't been optioned to the Minor Leagues since 2013.
"It was a tough one," manager Dave Roberts said of the decision. "Slyky has been a mainstay here for a number of years and has gone through a lot physically, with the inconsistent playing time for a role player. We acquired Franklin to hit off left-handed pitching and he's healthy. It gives Slyky an opportunity to get consistent at-bats and work through mechanical things. He'll be back at some point."
The Dodgers face two more difficult decisions later in the week, as center fielder Joc Pederson and second baseman Logan Forsythe are on rehab assignments with Roberts anticipating their return by Friday night's series opening in San Diego.
It has been assumed that a spot for Pederson would be opened by returning Cody Bellinger to Triple-A. But Bellinger has played well in his trial, and his start at first base Tuesday over the ailing Adrian Gonzalez opens speculation that Gonzalez could be headed to the disabled list for the first time in his career because of lingering right elbow tendinitis.
Roberts said he hasn't discussed the disabled list yet with Gonzalez, who showed more power during early batting practice than he has this season.
Ken Gurnick has covered the Dodgers since 1989, and for MLB.com since 2001.