Huong was accused alongside Indonesian Siti Aisyah, who was suddenly freed on Monday by a Malaysian court where the women were being tried.
Vietnam's Foreign Minister Pham Binh Minh called his Malaysian counterpart on Tuesday asking Huong to be released as well, according to state media.
As the court announced its decision, Siti Aisyah, 26, turned to her Vietnamese co-defendant, Doan Thi Huong, 30, in the dock and the two women, who had been facing the death penalty together, embraced in tears. Prosecutors may decide then to inform the court whether the application had been successful.
The call from Vietnam's foreign minister was an unprecedented public request from Hanoi, which generally does not get involved in criminal cases involving its citizens overseas.
They had claimed that they thought they were taking part in a prank for a television show.
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Ms Doan was due to testify yesterday after months of delay but the trial was adjourned after her lawyer said she was "traumatised" to learn she now faced the charges alone.
Once the court released her, Siti Aisyah, wearing a black traditional Malay dress and headscarf, was rushed to the Indonesian embassy, where she spoke briefly with journalists. "I don't know the details of what happened but the prosecution can withdraw the charge".
"We have lined up four to five defence witnesses should there be no favourable reply from the AG", he said.
Thomas wrote in a letter to Indonesia's minister of law and human rights that prosecutors chose to drop Aisyah's charges and release her "taking into account the good relations" between Malaysia and Indonesia.
Salim said Huong should also be accorded the same treatment although both were charged separately, but a joint trial was held.
"I have no information (regarding that)", he said, in response to questions at a press conference in Parliament, reported The Star.