Rose, 36, has played in 21 events since the PGA Tour season began in October, including Europe's Ryder Cup defeat.
The world number 11 was in discomfort because of a disc herniation at The Players Championship in May.
"I have decided to take the next eight weeks off for rest and recovery. At this point in my career, it's important to invest in my body," he said.
"This time off is crucial for me to return to peak performance."
The Englishman's Olympic win arrived after a number of players withdrew from the Games, citing concerns over the Zika virus and congestion in their season schedule.
The gold represented the only win of his season and he will now miss next week's British Masters and the European Tour's Race to Dubai finale in November.
Rose is one of four players to take turns in hosting the British Masters each year, along with Ian Poulter, Lee Westwood and 2016 host Luke Donald.

The Russian club, managed by former Chelsea and Tottenham boss Andre Villas-Boas, won their domestic league with two games to spare last weekend.
And just how did the Villas-Boas and his players celebrate? By dressing in traditional Russian clothing, as you do.
A picture was posted by former Manchester City player Javi Garcia on his Instagram account featuring a sharp-looking Garcia and his equally snappily-dressed team-mates, which includes former Arsenal forward Andrey Arshavin, surrounding Villas-Boas.
Zenit's title win, the fourth in their history, came in Villas-Boas's first full season in charge.
Olympic champion Justin Rose will miss the rest of the 2015-16 season to fully recover from a back injury.
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As far as team photos go, Zenit St Petersburg's will take some beating.