Sky said Rowe, 27, had fractured his tibia and fibula and was recovering from surgery at his home in Cardiff.
Rowe's brother, Matt, is due to marry Dani King, who won a gold medal in the team pursuit at the London 2012 Olympics.
"It's early days but I'm determined to get back racing as soon as I can".
Liverpool FC reveal £25m shirt sleeve sponsor
The deal will also result in Western Union becoming the club's first-ever official shirt-sleeve sponsor. Western Union become the sixth sponsor to adorn Liverpool's jerseys since their inception in 1892.
Speaking about the incident, he said: "I jumped down into the water but landed in a shallow section on my right leg. I knew straight away that it was a bad one".
But despite the seriousness of his injury and the substantial amount of pain it left him in, he insists he has no regrets about attending his brother's stag do and going white-water rafting.
"An injury like this is a test of character for anyone, but character is something Luke has plenty of".
"He's a really important part of our team and, as a team, we'll be right behind him throughout his recovery".
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