Shaw was reinstated from the 10-day injured list on Tuesday.
The Brewers made the move despite Hiura's solid performance at the plate. In 17 games in the majors, he hit .281 with five home runs and nine RBIs.
Shaw, who was placed on the IL on May 14 with a strained right wrist, was off to a slow start this season, batting just .163 with four homers and eight RBIs. He hit .235 with a home run and two RBIs in a 10-game rehabilitation assignment.
"We believe Travis has earned the right to play at the major league level," president of baseball operations David Stearns told reporters, according to the Journal Sentinel. "He's healthy. He has gone and done his rehab assignment. We believe it's time for him to come back.
"He has been an extremely productive player for us over the past couple of years, a player who has contributed a whole lot to the organization. And he has earned the right to be at the major league level."
Stearns indicated that the Brewers chose to make the move with Hiura because he had minor league options remaining.
"We always have to keep in mind that this is a long season and that preserving organizational depth, preserving options throughout the entire season, is something we think is really important," Stearns said, according to the Journal Sentinel. "It's something that we have focused on over the last couple years and it has served us well.
"We have players who are either performing now or have performed at a very high level in the past. It generally behooves us to make sure we have as much depth and flexibility as possible."
Hiura was the ninth overall selection in the 2017 draft and was rated by ESPN's Keith Law this season as baseball's No. 21 overall prospect.