Food store "Unico", located in the Lavalle district, is owned by the family of Messi's wife, Antonela Roccuzzo, who is also a native of the Argentina city.
Police were called to the scene after a reported 14 shots were fired at the store's shutters and front door in the early hours of Thursday morning.
Two individuals on a motorbike were seen fleeing the scene, after leaving a sinister message for the PSG forward.
"Messi, we are waiting for you," the note read. "Javkin is a drug dealer. He is not going to look after you."
The messages refer to Rosario's mayor, Pablo Javkin, who after the incident spoke out on the level of violence and need for more policemen in a city where crime is on the rise.
Rosario is the largest city in Argentina's central province of Santa Fe, 300 kilometres (186 miles) north of Buenos Aires.
No people were harmed in Thursday's attack, but significant damage is thought to have been done to the store.Getty Images
Messi won FIFA's The Best Men's Player 2022 at an awards ceremony in Paris on Monday, having led his nation to their third world crown in Qatar.
Argentina's 2022 World Cup triumph was, of course, Messi's first in an otherwise immaculate career, as he is widely considered as one of - if not the - greatest player of all time.
The 35-year-old recorded a mammoth seven goals and three assists during the tournament - including a brace in a pulsating final in Lusail - as he got his hands on the coveted trophy at the fifth time of asking.Getty
Messi's heroics in Qatar came a year-and-a-half after winning his first major international trophy, the 2021 Copa America in Brazil.
The reaction of Argentina's players at the full-time whistle - who ran to embrace Messi in unbridled joy - reflected the sentiment shared across the country for his endeavours over the years.
Because after years of hurt - including nearly calling time on his international career - Messi finally brought Argentina back to the top of the world stage. And for that, the PSG man enjoys hero status across his country and beyond.
No stronger is that felt than in his hometown of Rosario, where he left as a child to join Barcelona's famed La Masia academy. Murals eulogising his greatness are commonplace, such as the 100ft-tall masterpiece unveiled after Argentina's Copa America triumph.Getty Images
Roccuzzo's ties with Rosario are also strong. The 35-year-old grew up in Santa Fe's largest city alongside Messi, where it is thought the couple's relationship blossomed from 2007 onwards. They even returned to their hometown back in June 2017 to get married in a star-studded ceremony.
Thursday's attacks, then, are all the more harrowing given the strong connection to Rosario shared by both Messi and his wife, especially considering the specific target on Roccuzzo's family's business.
Thus far, neither Roccuzzo or Messi have commented on the matter. The couple are now based in Paris with their three children, with PSG next in action on Saturday at home to Nantes.