Colleagues and friends have begun sharing tributes on social media, with Labor leader Anthony Albanese saying the party was in shock at the tragic news.

"My sincere condolences to her family. Kimberley will be missed by us all," he said on Twitter.

Former Labor leader Bill Shorten said Senator Kitching suffered from "a heart problem" on Thursday evening in Melbourne and died soon after.

Mr Shorten said her passing was an immense loss to Labor and the nation.

"To know Kimberley was to be touched not just by her serene intellect but her incredible warmth and vivacity," he said in a statement.

"As a Labor senator she was relentlessly energetic and conscientious recently resulting in international recognition for her human rights work.

"Our hearts go out to her husband Andrew, her family and loved ones."

Labor MP Madeleine King wrote about how much she would miss the senator.

"She was a steadfast and supportive colleague. Smart, hardworking, dedicated, funny and fun to be around," she wrote on Twitter.

"I wish I had told her that. I'll miss coffees shared at Aussies & around the building. I'll miss Kimberley."

Senator Kitching joined the Senate in 2016 and was a member of the Labor party for almost three decades.

She was born in Brisbane in 1970 and became a Melbourne councillor between 2001 and 2004.

Senator Kitching also worked as a general manager at the Health Workers' Union and as a special counsel at legal firm Cornwall Stodart.

She chaired parliament's Foreign Affairs, Defence and Trade References Committee and was the deputy chair of the Foreign Affairs, Defence and Trade Legislation Committee.

Prime Minister Scott Morrison said the senator was a "serious parliamentarian who had a deep interest in Australia's national security".

"She had a passion about Australia's national interest and argued for it," he said.

"She demonstrated that her passion for her country was always greater than any partisan view. She clearly loved her country and it genuinely showed."

Mr Morrison said Senator Kitching "followed her conscience and was fearless".

"She was respected by those on both sides of the Parliament - she was a parliamentarian in the truest sense. Senator Kitching was deeply respected by the Coalition," he said.

"To Senator Kitching's family, I extend the sympathies of the government."

Deputy Prime Minister Barnaby Joyce said the senator was a beautiful woman and her death was a tragic loss.

"I am deeply, genuinely and so terribly upset to hear the tragic news about a dear person and dear friend, Senator Kimberley Kitching," he said.

"I know she is with our Lord, and I offer my sincerest and deepest condolences to her family."

Liberal senator James Paterson said she was a "true patriot".

"She was a warrior for her cause, a friend of freedom and a true patriot who had an enormous impact in her short time in the Senate," he said.

"A huge loss to the parliament, the ALP and her family."

Australian Associated Press