Writing in The Times on Wednesday, Mr Sacks said: "We may not agree with the Vatican line on homosexuality. But the State is trampling on our rights as individuals."
The Pope told bishops from England and Wales that the Government's equality legislation had served to "impose unjust limitations on the freedom of religious communities to act in accordance with their beliefs".
His attack came a few days after Church of England bishops in the House of Lords helped to vote down an amendment that would have narrowed the exemptions for religious organisations in existing equality employment laws.
Mr Sacks said he did not believe religious beliefs were entitled to privileged status in a democratic society but warned that using the ideology of human rights to "assault" religion risked "undermining the very foundation of human rights themselves".
"There are times when human rights become human wrongs. This happens when rights become more than a defence of human dignity, which is their proper sphere, and become instead a political ideology, relentlessly trampling down everything in their path," he said.
"This is happening increasingly in Britain, and it is why the Pope's protest against the Equality Bill, whether we agree with it or not, should be taken seriously."
He said the dismissal of a nurse for offering to pray for a patient, the closure of Roman Catholic adoption agencies for refusing to place children with same-sex couples, and the branding of a Jewish school's admissions policy as racist were evidence that Britain was entering "dangerous territory" over human rights.
"When Christians, Jews and others feel that the ideology of human rights is threatening their freedoms of association and religious practice, a tension is set in motion that is not healthy for society, freedom or Britain," he said.
"Rather than regard the Pope's remarks as an inappropriate intervention, we should use them to launch an honest debate on where to draw the line between our freedom as individuals and our freedom as members of communities of faith. One should not be purchased at the cost of the other."