Dr Smith has previously warned that the NHS is “eerily quiet” for illnesses other than the virus and expressed concerns about seriously ill people not going to hospital.
The number of people who died in Scotland from all causes a fortnight ago was 1,969, much higher than the average of 1,100 for the same week over the last five years.
However, coronavirus accounted for only 608 of the 869 additional fatalities, leaving 261 of the surplus unexplained.
Dr Smith said there was “strong evidence” that people refusing to approach their GP has led to the vast reduction in urgent cancer referrals.
“This is seen not just in Scotland but appears to be a pattern that is seen in other parts of the UK too,” he said.
“GPs are telling me that they are seeing much fewer people coming forward with these types of symptoms and signs, and the volume of referrals that are being received backs this up.”
On an average week, he said there would normally be around 2,700 urgent suspected cancer referrals in Scotland but this plummeted to 744 last week.
He said the number of referrals has continued to drop during the outbreak, with 948 recorded the week before last.
“I don’t believe for a second that these diseases or these concerns have simply disappeared, so it leaves me worried that there are people out there who are not seeking help from their GP when they need it,” he added.
“My message is don’t ignore it – if it was urgent before Covid-19, it remains urgent now.”