Lewicki was optioned to the alternate site Sunday.
Lewicki's contract was selected by the Diamondbacks on Tuesday.
Lewicki will be a part of the Diamondbacks' 60-man summer camp.
Lewicki (elbow) was sent outright to Triple-A Reno on Tuesday.
Lewicki (elbow) was transferred to the 60-day disabled list Sunday.
Manager Ron Gardenhire said Thursday that Lewicki (elbow) will undergo Tommy John surgery next week and miss the entire 2019 season, Evan Woodbery of MLive Media Group reports.
Lewicki is scheduled to see an elbow specialist, Evan Woodbery of MLive.com reports.
Lewicki underwent an MRI on Wednesday that confirmed a bone spur but no additional damage to the elbow, Jason Beck of MLB.com reports.
Lewicki was placed on the 10-day disabled list with right elbow inflammation Wednesday.
Lewicki did not factor into the decision in Monday's win over the White Sox, as he allowed three earned runs on six hits over 4.2 innings. He walked three and struck out three.