Mengden, who is 1-4 with a 4.54 ERA in six starts for Oakland, was likely going to start in Sunday's series finale before Hill's blister issue.
Hill is 9-3 with a 2.25 ERA in 13 starts this season.
Cash Kruth is a reporter for MLB.com. Follow him on Twitter at @cashkruth. This story was not subject to the approval of Major League Baseball or its clubs.