He said Burrow would “continue to inspire me every single day”.
Sinfield added: “I would always say that you were pound for pound the toughest player I ever played alongside, however since your diagnosis, you were the toughest and bravest man I have ever met.”
He signed off his tribute by saying: “I will miss you my little mate, all my love, Kev x.”
Sinfield has raised millions alone for MND by undertaking a series of endurance challenges.
Last year he completed seven ultra-marathons over seven days in seven cities, including Dublin, Edinburgh and Birmingham, raising over £825,000.
The tight-knit pair also launched the Rob Burrow Leeds Marathon, which took place for the second time last month.
Earlier this year, Burrow and Sinfield contributed to a picture book which told the story of a friendship between two young boys named Rob and Kev.
In 2022, Burrow was presented with the Helen Rollason Award at the BBC’s Sports Personality of the Year ceremony, with Sinfield also recognised with a special award.