The encounter happened inside a hallway at Fiserv Forum after Antetokounmpo and the Bucks eliminated the Boston Celtics in the Eastern Conference semifinals.
The meeting of the Milwaukee stars occurred about six months after Yelich won the 2018 NL MVP award.
Now, Antetokounmpo could bring another MVP trophy to the city situated on Lake Michigan's western shore.
The Bucks forward is a finalist for NBA MVP along with Oklahoma City swingman Paul George and Houston guard James Harden, who won the award last season.
The winner will be announced Monday night.
"Obviously I'm happy to be one of the three finalists," Antetokounmpo said two days after losing to the eventual NBA champion Toronto Raptors in the Eastern Conference finals. "Hopefully I get it. If not, I have many more years to be able to help my teammates be successful and put me in a situation that we can get it."
Antetokounmpo set career highs by averaging 27.7 points, 12.5 rebounds and 5.9 assists while leading the Bucks to a league-best 60-22 record in the regular season. The 6-foot-11 first-team All-NBA performer is just the second player in league history to average at least 27 points, 12 rebounds and 5.5 assists, joining Oscar Robertson during the 1961-62 campaign.
The 24-year-old Athens, Greece, native would be only the fifth international NBA MVP, joining Dirk Nowitzki, Steve Nash, Tim Duncan and Hakeem Olajuwon.
Yelich won the NL MVP award in near-unanimous fashion in November after becoming the first Brewers player to win a batting title. He finished two home runs and an RBI shy of the NL's first Triple Crown since the St. Louis Cardinals' Joe Medwick in 1937.
The Thousand Oaks, California, native garnered 29 of 30 first-place votes from the Baseball Writers' Association of America to win in a landslide over Javier Báez of the Chicago Cubs and third-place finisher Nolan Arenado of the Colorado Rockies. The other first-place vote went to New York Mets pitcher Jacob deGrom, who finished fifth in the MVP balloting a day after winning the NL Cy Young Award.
Yelich, 27, called his MVP victory "mind-boggling" and told The Associated Press he's rooting for Antetokounmpo to bring the NBA's top individual honor back to Milwaukee.
"It'll be cool," said Yelich, who is in the midst of yet another MVP-caliber season. "It's definitely unique. It doesn't happen all the time when you have two guys that have won an MVP in the same city in different sports. It's definitely exciting times for Milwaukee and sports fans here."
Having the NBA and NL or AL MVP award winners in the same city at the same time isn't the rarest of occurrences.
Harden and José Altuve accomplished the feat in Houston in 2018 after the Astros second baseman won the 2017 American League MVP. It also happened for Houston in 1994 with Olajuwon and Hall of Famer Jeff Bagwell.
Chicago also has seen it happen a couple times: Michael Jordan and Sammy Sosa in 1998, and Andre Dawson won the NL MVP in 1987 followed by Jordan taking the 1988 NBA MVP honor.
Roger Clemens and Larry Bird did it in Boston in 1986, and Mike Schmidt and Julius Erving were the toast of Philadelphia in 1981.
The script also worked out perfectly for Los Angeles when Kirk Gibson won the 1988 NL MVP and Magic Johnson captured the 1989 NBA MVP.
But all of those most valuable overlaps occurred in major media markets, and Milwaukee is one of the smallest markets in major North American professional sports.
Brewers manager Craig Counsell, who grew up in Whitefish Bay, Wisconsin, said having both the NL MVP and NBA MVP in Milwaukee would be a huge victory for a city and a pair of fan bases that saw both the Brewers and Bucks fall just short of winning world championships in the last few months.
"We're all hoping for it," he said. "I think everybody in the state's hoping for it. I know Milwaukee's hoping for it. It would be really cool. As a sports fan, we're lucky to be able to see two of the best doing their jobs in their profession in our city. It makes both teams exciting."
Antetokounmpo would be only the second Bucks player to win the honor, joining Kareem Abdul-Jabbar, who won three of his record six MVP awards while playing for Milwaukee in the early 1970s.
Bucks coach Mike Budenholzer, who is a finalist for NBA Coach of the Year, said Milwaukee is fortunate to have a player like Antetokounmpo, who is also a candidate for NBA Defensive Player of the Year.
"For our fan base and for our organization to have an MVP, it's very rare, and hopefully we all appreciate it and enjoy having a great, great player like Giannis," he said. "It's just incredible what we have in Giannis."
As for any advice Yelich may have for Antetokounmpo if he wins: "I don't think he needs any advice from me," he said. "He's a great kid. He carries himself really well. Just from the times I've gotten to interact with him, he seems great. He seems like he's going to handle it very well."