This could mean a shut-down of all mobile telephone services in the Mediterranean coastal enclave.
"Public prosecutor Ismail Jabr has issued an order for the closure of the Jawwal company's headquarters as a preliminary measure against it for tax evasion," his office said in a statement.
It warned that all other "tax dodgers will be pursued in earnest," a possible reference to banks operating in Gaza, which is controlled by the Islamist movement.
It was unclear when the offices would be closed.
An executive from Jawwal, one of the principle telecoms providers in the Palestinian territories, insisted that "the company is not avoiding any of its (payment) commitments."
Business analyst Omar Shaaban said the closure could mean cessation of all mobile phone services in Gaza.
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"There is no alternative in Gaza to the services provided by this company," he told AFP.
Shaaban said it was likely Jawwal was paying taxes to the West Bank-based Palestinian Authority and not the Hamas authorities in Gaza.
A years-long split between Hamas and the PA, which is dominated by rival political party Fatah, has caused previous financial crises in the war-wracked territory.
Last year, Hamas closed banks for several days after a dispute with the PA over wages.
Under an April 2014 unity agreement, Hamas and Fatah were to put their differences behind them, transferring adminstration of Gaza to the PA, including collection of taxes and running of ministries.
But the PA refused to pay the salaries of tens of thousands of officials appointed by Hamas since it took over Gaza in 2007, causing the unity deal to fail and leaving Hamas de facto in charge of Gaza.
A war in Gaza between Hamas and Israel last summer caused further setbacks to any Palestinian reconciliation.