Sylvester Stallone's wife, Jennifer Flavin, filed for divorce after a huge argument over whether Sly could get a new dog, TMZ has learned.

Sources directly connected to the couple tell TMZ, the "Rocky" star wanted to get a Rottweiler for protection -- protection for their family -- but Jennifer did not want another dog. We're told the 2 were at loggerheads over the pooch, and they each fiercely stuck to their positions.

Our sources say they had an extremely heated argument that brought up other issues, although we're told none of those issues appeared to be marriage-enders.

Sly ended up getting the dog named Dwight ... also the name of his character on his new show "Tulsa King." Sly posted videos and photos of him with Dwight this month on Instagram, with the caption ... "So incredibly happy with my newly acquired four legged friend ”DWIGHT“ my characters name from the Series, keep punching and keep barking !!! Thank you very much to Trainer and breeder Dave Smith and his wonderful wife !!!"

Three days later, he posted this pic with the caption ... "”DWIGHT” Definitely a true friend! KeepPunching And Keep barking!"

Sly has been in Oklahoma shooting his show, and we're told he was shocked -- SHOCKED -- when he learned Jennifer filed for divorce. We're told Sly felt they could work out their differences.

This explains the tattoo on Sly's arm ... he put a Rottweiler on his arm over the tattoo he had of Jennifer. The photo surfaced Monday on DailyMail, but that was AFTER Jennifer filed divorce docs -- that happened last Friday.

Our sources say there was no evidence a war was brewing. In fact, the family was together July 30 to celebrate Frank Stallone's birthday, and sources tell us they all seemed happy.

As we reported, Jennifer claimed in her divorce docs Sly was improperly either spending or moving martial money around. Our sources say Sly flatly denies that.

It's problematic on many levels. We've learned they have been shooting a 10-episode reality show about Sly, Jennifer and their daughters ... they've already shot 9 episodes so the fate of that is unclear.