A Tuesday deadline had been set for the test, which is being sought by celebrity photographer Larry Birkhead, who claims to be the biological father of Smith's four-month-old baby Dannielynn.
Smith's attorney, Ronald A. Rale, questioned the legality of the test, claiming authorities in the Bahamas, where his client is now living, needed to grant work permits before an American doctor could conduct the test.
The judge granted a stay, pending a Feb. 7 hearing.
Birkhead's attorney, Debra Opri, called Rale's request "a delay tactic."
Smith claims the father of her baby daughter is her longtime personal lawyer Howard K. Stern.
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