The Asharq center for human rights said in a statement that Nemr, who has been on a hunger strike since mid-July, is now in declining health.
The human rights group went on to call on Riyadh to release the cleric immediately and without any preconditions.
It says the Saudi regime is responsible for any injury that is inflicted on Sheikh Nemr while in detention.
The Shia cleric was injured and arrested by Saudi forces while driving to his home on July 8. His family members say he has been badly tortured while in detention.
Sheikh Nemr’s arrest sparked massive protests, with angry demonstrators demanding his immediate release.
Since February 2011, protesters have held demonstrations on an almost regular basis in Saudi Arabia, mainly in the Qatif region and the town of Awamiyah in Eastern Province, primarily calling for the release of all political prisoners, freedom of expression and assembly, and an end to widespread discrimination.
However, the demonstrations have turned into protests against the repressive Al Saud regime, especially since November 2011, when Saudi security forces killed five protesters and injured many others in Eastern Province.
Similar demonstrations have also been held in the capital, Riyadh, and the holy city of Medina over the past weeks.
According to Human Rights Watch, the Saudi regime “routinely represses expression critical of the government.”