Earlier, second baseman Jonathan Herrera was recalled from Triple-A Colorado Springs and inserted into the Rockies lineup against the
San Francisco Giants. Clint Barmes, who has started 10 games at second base for Colorado, played shortstop in Tulowitzki's absence.
To make room for Herrera the Rockies placed right-hander Kip Wells on the 15-day disabled list with a blood clot in his pitching hand. Wells left the team Tuesday to see a hand specialist in Denver, where the diagnosis was made.
Grilli, who is 0-1 with a 3.29 ERA, was acquired for minor league right-hander Zach Simons.
"Jason adds a quality arm to our club," general manager Dan O'Dowd said. "He can do a variety of different things in our bullpen."
De La Rosa was player to be named later in the deal that sent right-hander Ramon Ramirez to the Royals in March. De La Rosa, 27, was 3-0 with a 1.64 ERA at Triple-A Omaha and will be assigned to Colorado Springs.
Tulowitzki might also be headed for the DL.
The Rockies' 23-year-old shortstop was injured during the first inning of Colorado's 3-2 win over San Francisco on Tuesday. Tulowitzki seemed to initially hurt himself while throwing to first base on Eugenio Velez's grounder then later aggravated it while bending over to stop Aaron Rowand's single.
He grimaced and grabbed his left hip and lower back area before walking gingerly off the field while accompanied by the Rockies' athletic trainer. The injury was later diagnosed as an upper left quadriceps strain.
Tulowitzki is batting only .152 with one home run and 11 RBIs.