Burrow revealed last week that he had been diagnosed with motor neurone disease (MND) of which there is currently no known cure.
The 37-year-old won eight Grand Finals, three World Club Challenges and two Challenge Cups in 17 years during a glittering career with the Rhinos.
Burrow retired from playing at the end of the 2017 season, winning an eighth Super League Grand Final in his last game.
Fans quickly rallied in support after the announcement of his diagnosis, raising more than £50,000 for Burrow and his family in just one day.
On Saturday evening, the fundraiser on VirginMoney has reached a £200,000 target with more than 9,000 people donating to the cause.
The fund will support Rob in his treatment and help his wife and three young children, all under the age of eight, in the years ahead.