The prizes for defensive excellence were announced by Rawlings for the 60th time.
"Obviously, five, it's a pretty special number," Arenado said. "It means a lot. ... Right now I want to try to win as many as I can while I'm healthy."
Heyward joins Andre Dawson as the only Cubs outfielders to win consecutive Gold Gloves, according to ESPN Stats & Information.
This year's honorees feature 12 previous winners and six first-time winners:
SS Andrelton Simmons, Los Angeles Angels - 3rd award
LF Alex Gordon, Kansas City Royals - 5th award
CF Byron Buxton, Minnesota Twins - 1st award
1B Paul Goldschmidt, Arizona Diamondbacks - 3rd award
2B DJ LeMahieu, Colorado Rockies - 2nd award
3B Nolan Arenado, Colorado Rockies - 5th award
RF Jason Heyward, Chicago Cubs - 5th award
The World Series champion Houston Astros and NL champion Los Angeles Dodgers were both shut out. Astros pitcher Dallas Keuchel had won the past three years. Meanwhile, the Twins were represented by two first-time winners in Buxton and Dozier.
"This is a special moment," Buxton said.
Barnhart, the first Reds catcher to win since Hall of Famer Johnny Bench in 1977, also became the second different catcher (the San Francisco Giants' Buster Posey won in 2016) to win in the NL in the past two years after the St. Louis Cardinals' Yadier Molina won eight straight at the position. Posey and Molina were again nominated this year.
"It's as good as it gets for me. I'm a defensive guy, and I take a lot of pride in that," Barnhart said. "I am taken aback by it, to be honest with you. ... Buster and Yadi are obviously two of the best guys in baseball."
The Angels' Maldonado snapped Salvador Perez's four-year winning streak for AL catcher.
The "Best of the Best" honor -- voted on by fans --- will be unveiled Friday and will be given to one AL winner and one NL winner.
Additionally, Derek Jeter will be recognized with the Rawlings Heart of Gold Award and Reggie Jackson will be honored with its Lifetime Achievement Award. Omar Vizquel and Ivan Rodriguez will also be inducted into the Rawlings Gold Glove Award Hall of Fame.
The Associated Press contributed to this report.