Her husband was arrested together with another Turkish national, Turgay Karaman, last week.
"I am begging the Malaysian government and police not to deport him," Ainnurul Aisyah Yunos told a news conference.
Her husband Ihsan Aslan was arrested together with another Turkish national, Turgay Karaman, last week under a security law which allows detention without trial for 28 days.
Malaysia's deputy prime minister Ahmad Zahid Hamidi has said anti-terrorism police had been investigating the two men, along with others, for "spreading, influencing and funding" activities by the Islamic State group.
But rights groups fear Malaysia may be responding to pressure from Turkey, which has mounted a huge crackdown on perceived opponents since a failed coup against President Recep Tayyip Erdogan last year.
"I am not angry against anyone. This is a huge misunderstanding. He is not guilty. I hope he will be released soon. We are worried about his well-being," said Aisyah, who is Malaysian.
The 35-year-old, who broke down in tears several times, was accompanied by her three young children -- one of whom is a special-needs child.
Two days after the arrest of Aslan and Karaman, Turkish academic Ismet Ozcelik was also detained -- ostensibly for national security reasons.
Turkey's state-run news agency has said the three men were linked to US-based preacher Fethullah Gulen, accused of organising the coup attempt.
Aisyah denied her husband had any questionable links.
In a statement handed to reporters, she said her husband "has always been loyal to the lawful government of Turkey and has never been involved in any illegal activity threatening the democracy of Turkey or Malaysia."
Erdogan's government has detained or sacked tens of thousands of people under a state of emergency imposed after the attempted power grab.
The crackdown focuses on alleged supporters of Gulen.
The UN Human Rights Office for South-East Asia last Friday expressed serious concern about the arrests and urged Malaysia to refrain from deporting the men to Turkey.
"There are concerns that these men may have been targeted over their suspected links to the Gulen movement..." said Laurent Meillan, acting regional representative, in a statement.