David Taylor, the husband of East Kilbride and Strathaven MP Reid, and two other men were arrested by counter-terrorism officers at addresses in London and Wales.
Taylor is accused of assisting a foreign intelligence service, which he denies.
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On Thursday evening, a Labour Party spokesperson said: “Joani Reid has agreed to fully cooperate with the Labour Party’s investigation into these matters.”
In a statement, the now independent MP said: “This week has been the worst of my life. The shock of recent days has been difficult for me and my family.
“I want to reiterate something very important: I am not under investigation by the police and no accusations have been against me. I have done nothing wrong.
“I love my country. To serve the people of East Kilbride and Strathaven as their MP and the Labour Party has been – and continues to be – the privilege of my life.
“I understand that speculation and gossip is fevered at a time like this. I do not want the circumstances that I and my family find ourselves in to be a distraction for this government, of which I am proud and in whom I believe.”
She added: “I also do not want my children – who have nothing to answer for and who deserve privacy and compassion – to find themselves subject to intrusion.
“Following discussions with the chief whip, I am voluntarily suspending myself from the whip this evening and will not sit as a Labour MP until internal investigations are concluded. I will welcome and cooperate with any questions and worries the party may have.
“I, and my team, will continue to serve my constituents in the normal way as their Member of Parliament.”
Reid is the granddaughter of trade unionist Jimmy Reid and served as a councillor in Lewisham, south London, for eight years before becoming an MP.
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Elsewhere, James Robinson, a former aide to ex-Labour deputy leader Lord Tom Watson, has said police searched his home in relation to the arrests.
Robinson, director of Woburn Partners consultancy, said he was not detained, arrested or questioned.
“I can confirm that police officers visited my home yesterday with a search warrant. I understand their attendance was part of enquiries into those arrested and questioned over matters allegedly relating to China.
“Naturally, I co-operated fully with the police and will, of course, continue to do so as long as their investigations into the possible wrongdoing of others continues.
“I would like to make it absolutely clear that I have neither been detained, arrested nor questioned in connection with this, or any other, matter.”