The pair met shortly before the 2010 World Cup in South Africa when Pique featured in the music video for the tournament’s official song, which was sung by Shakira.
The 45-year-old Colombian singer and the 35-year-old FC Barcelona defender have been together for 11 years and share two children, nine-year-old Milan and seven-year-old Sasha.
“We regret to confirm that we are separating,” they said in a joint statement released through their PR agency.
“We ask that you respect our children’s privacy because their well-being is our top priority.”
The two met just before the 2010 World Cup in South Africa, when Pique appeared in the music video for Shakira’s Waka Waka, the tournament’s official song (This Time for Africa).
It comes as the Hips Don’t Lie singer faces a trial over alleged tax fraud charges in Spain after she lost an appeal last month.
Prosecutors claim she failed to pay up to 14.5 million euros (£12.4m) in tax on income earned between 2012 and 2014.
Her legal team has said they will keep defending her case with solid legal arguments.
“Shakira’s conduct on tax matters has always been impeccable in all the countries she had to pay taxes and she has trusted and followed faithfully the recommendations of the best specialists and advisers,” they said in a statement.