Visa announced the hire in a blog post Friday.
Square's shares went slightly negative, about 1 percent, after the announcement.
Bowman's departure from Square comes just months after CEO Jack Dorsey lost key deputy and CFO Sarah Friar, regarded by Wall Street as a "rockstar CFO."
Bowman was a big hire for Square in 2015. She came from Amazon, where she spent more than a decade on the tech giant's payments team.
Square may be losing key executives but it's also hiring new ones.
Last week, Square tapped Amrita Ahuja as its new CFO, succeeding Friar. In an interview with CNBC, Dorsey said he wanted to showcase more of Square's bench of executives.
Correction: Mary Kay Bowman was Square's head of payments. A previous version misstated her title.