Group convener Anas Sarwar said the cross-party group's report was an "urgent wake-up call" for the government.
He told the BBC's Good Morning Scotland that a shortage of radiologists meant patients had to wait longer to be diagnosed so they can begin their cancer treatment.
"This is a global shortage of workforce, but the specific challenge we have in Scotland is that cancer is our biggest killer," the MSP said.
"We are going backwards in terms of the vacancy rates, we are going backwards in terms of the six-week treatment time."
He added that a "comprehensive workforce plan" promised by the Scottish government in the summer of last year had been delayed until early next year.
Mr Sarwar said ministers needed to consider how to attract, train and retain domestic and international staff, how to stop early retirements in the sector and bring down locum fees.
Cancer Research UK chief executive Michelle Mitchell said the Scottish government must "publish a long-term cancer workforce plan" to enable the NHS to prepare for rising demand in the future.
She said: "The findings of this inquiry are deeply concerning.
"Diagnosing cancer early can make all the difference, but there are major shortages in the staff trained to carry out the tests that diagnose cancer.
"Cancer services in Scotland are already struggling. Without urgent action, this will only worsen as demand increases."
'Waiting for my diagnosis was such an anxious time'
Tom Martin, from Edinburgh, said he waited about three months to start his cancer treatment, something he fears may have given the disease in his prostate time to spread.
Mr Martin, who has now been given the all-clear, said: "NHS workers do an amazing job and I'm so grateful for the treatment and care I received. But cancer services are stretched to the limit, something which is only going to get worse as more people are diagnosed with cancer.
"Waiting for my cancer diagnosis and treatment was such an anxious time, for me and my family. You don't know where you stand and there are times you fear for the worse.
"I know that if cancer is diagnosed at an early stage, the more successful the treatment is likely to be.
"I do wonder if I had been seen earlier, would the prostate cancer have been caught sooner, before it had spread. Who knows?
"The Scottish government must not shy away from making long-term plans that will ensure cancer services are able to cope now and in the future.
"People like me will depend upon it."
Responding to the report, Health Secretary Jeane Freeman said cancer was an "absolute priority for the Scottish government".
"Our £100m cancer strategy is focused on improving survival rates and ensuring we have the right workforce," she said.
Citing a "downward trend in cancer mortality rates" since 2009, Ms Freeman added: "More people are surviving cancer than ever before.
"Early detection of cancer is crucial to this continued improvement which is why last year the Scottish government launched a £850m waiting times improvement plan," she said.
Part of this funding would be spent on increasing numbers of staff and CT and MRI scanners to reduce waiting times for patients needing urgent treatment.
Ms Freeman added: "It is important to note that Scotland will be the first nation in the UK to offer a key support worker to help with the financial, emotional and wider impacts of living with cancer in recognition of the wider impact on patients and their families."