Sjostrom stood alongside Margaret MacNeil and Emma McKeon on the medal podium with a message of support for the Japanese swim queen, a major rival of all three, scrawled on their palms.
"Never give up, Rikako Ikee," read the tribute, alongside two love hearts, as the three 100m butterfly medallists held their hands out to the camera.
"I hope really that she (Ikee) will battle this cancer. She is a real fighter and the real winner," said Sjostrom.
The 25-year-old Swede had been looking to become the first female swimmer to win five gold medals in a single individual event but was forced to settle for silver after a stunning race by MacNeil.
But Ikee's illness puts her disappointment into perspective, she said.
"What is swimming compared to what she is going through? I told myself that before my race: it doesn't matter where I come because her battle is 50 times more than anyone else in this final," she added.
"I really hope she will recover and come back and do what she loves. She loved swimming so much and I really think she will come back and fight this cancer."
Canada's MacNeil, who at 19 is the same age as Ikee, said she and Australia's McKeon been easily persuaded by Sjostrom's idea to reach out to the Japanese star.
"She (Ikee) couldn't be here with us today so we're hoping that this will show we're supporting her and we're here if she needs anything," she said.
Ikee, the poster girl for the 2020 Tokyo Olympics, was diagnosed with the cancer earlier this year and is receiving treatment in Tokyo.
The teenager shot to fame last year at the Asian Games when she secured a record six gold medals.
But she tweeted in February that she had been diagnosed with leukaemia after experiencing problems during a training camp in Australia.
She has since said that battling the disease has proved "thousands of times harder" than she expected.
The young star would have been a favourite to win 2020 Olympic gold in the 100 metres butterfly and a serious medal contender in the 200m freestyle in her home city.
Japanese media said the country's main bone marrow bank was flooded with donation inquiries after Ikee reported her diagnosis.