Mr Shorten said he got a "dreadful" call from Andrew Landeryou on Thursday night saying she was gone.
"We raced over to this street in Strathmore where she had pulled up in the car, where she experienced a heart attack, and we waited with her husband until the undertaker's car came, which was terrible," he said on Friday.
"I feel for her husband most of all. They had each other, and now one half of two people has gone."
Mr Shorten said Senator Kitching was a fierce and warm person who spoke her mind with real honesty.
"She is the reason why we have very strong laws against corruption by foreign gangsters who then park their money in Australia," he told the Nine Network.
"It's a dreadful loss, at 52 she's been taken far too young."
Colleagues and friends shared tributes on social media on Thursday night, 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.
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 noted Senator Kitching was a practising Catholic and "we witnessed her authentic faith in the life of the parliament".
"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."
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.
