Church leaders also said the measures seemed to be an "attempt to weaken the Christian presence in Jerusalem". Church officials only said that it would be until further notice.
Jerusalem Mayor Nir Barkat said on Twitter that the tax did not include places of worship and that it was "illogical" to expect church-owned commercial property to keep on being tax-exempt.
State Minister for Media Affairs Mohammad Momani expressed the Kingdom's rejection of the "systematic" measures by the Israeli authorities to alter the historical and legal status quo that exists in the holy city including the confiscation of properties and bank accounts of the city's churches by the so-called "Jerusalem Municipality" under the pretext of not paying dues.
The church, where Jesus is believed to have been crucified, buried and resurrected, is one of Christianity's holiest sites.
The heads of Jerusalem's holy churches chose to implement the dramatic move in protest against the municipality's intention to collect property tax from church-owned properties that are not being used as houses of prayer and the Knesset bill that seeks to allow the state to confiscate properties sold by the churches since 2010 and compensate the owners.
Christian leaders say the proposed law would make it harder to sell Church land, a key source of funds.
Rachel Azaria, the lawmaker who sponsored the legislation, said in a statement she agreed to delay the committee's discussion by a week so that "we could work with the churches" to try to resolve the dispute.
The Jerusalem municipal authority is claiming that church-owned businesses and property which are not used as houses of prayer should not be able to enjoy a break from local property taxes.
The top clerics blasted the proposed Israeli legislation as "abhorrent... discriminatory and racist", saying that "this reminds us all of laws of a similar nature, which were enacted against the Jews during dark periods in Europe".
The government spokesperson noted that these measures violate worldwide and humanitarian laws and arrangements of the historical situation that has been existing for many years in this regard, as churches have always been exempted from paying such taxes to the city's civic authorities.
Al-Qawasmi called for a firm worldwide stance against the Israeli measures that contravene all conventions on Christian holy sites in the occupied city. "These are not houses of worship", it said in a statement. As for the future of the holy site, "we will decide when and how the church will re-open", they added.
The decision to close the church was extremely rare.
Media captionAdeeb Jawad Joudeh Al Husseini's family have been custodians of Church of the Holy Sepulchre for generations.
Jerusalem's famous Church of the Holy Sepulchre has shut indefinitely in an unprecedented move amid a fierce row with the Israeli government.