The federal MP said he got a call on Thursday night from Senator Kitching's husband Andrew Landeryou saying she had died.
"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," a teary Mr Shorten told the Nine Network 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."
MPs and colleagues from across the political spectrum have paid tribute to Senator Kitching in the wake of her sudden death.
Labor deputy leader Richard Marles said the senator's death was shocking and tragic.
"Kimberley was bright, she had a clear sense of what was right and wrong, she was a fierce advocate," he told the Nine Network.
"It feels unbelievable we are talking about Kimberley in the past tense."
Labor leader Anthony Albanese said the party was in shock at the 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."
Defence Minister Peter Dutton described the late senator as one of the very best in parliament.
"She was a real hawk on national security and I think the parliament will miss her," he said.
"Our country's poorer for her passing, at 52, it's devastating, obviously, for everyone who knew her."
Mr Shorten said Senator Kitching's death from a suspected heart attack was a wake-up call for all Australians aged over 50.
"None of us are bullet proof, bad things happen to good people, and just get your heart checked out," he said.
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.
