The Spanish-born footballer-turned-football agent revealed the news on Instagram.
“Sorry I haven’t been around much, it has been the toughest few weeks of my life,” the 32-year-old said.
“Within the space of one month I have found out the news that I have a rare brain tumour and had surgery to have it removed, I am now in recovery and so thankful. Life is too precious.”
Liverpool FC said in a statement that the “thoughts of everyone” were with Enrique.
“Everyone at Liverpool FC wishes him a full and speedy recovery and we look forward to seeing him back at Anfield again soon,” it said.
“You’ll Never Walk Alone, Jose.”
Enrique started his football career in Spain with Levante, before going on to play for Valencia, Celta de Vigo and then Villarreal.
He then spent four years at Newcastle and five years at Liverpool, before retiring in 2017.