Allan Wilson revealed signs of problems with supplies of the tests from Roche Diagnostics started to emerge last week.
Sky News has learned that thousands of patients could miss out on vital blood tests and screening because of the breakdown in the supply chain to the NHS.
Roche Diagnostics confirmed to Sky News that problems at its distribution warehouse in Newhaven in East Sussex means GPs and hospitals will have to ration blood tests and screening for diseases including cancer and diabetes.
Sky News understands that Roche built this new automated warehouse to increase capacity ahead of Brexit.
Mr Wilson, who heads up the IBMS, said scheduled deliveries of products used in testing for COVID-19 "and a wide range of other conditions" have not taken place as a result of the problems.
He added that Roche also supplies reagents for blood gas analysers, which are vital for treating people with respiratory illnesses, including COVID-19.
"This could turn out to be a significant issue," he said.
Calling the problem a "logistical failure", Mr Wilson said Roche and the NHS are working very hard to plug urgent gaps, but can only do that for a few days before it really starts to have a significant impact.
Dr Phil Williams, a GP in Lincolnshire, has been told to "pause testing" of routine blood samples. This includes check-ups for patients on long-term medication.
He told Sky News: "It's a nightmare. We are concerned about delaying annual patient reviews that may have already been delayed by COVID. It means complications will go undetected as medications are not monitored."
Sky News understands that Roche will not be able to supply chemical reagents, swabs and screening kits to affected NHS trusts and labs.
It means that all testing hit by the shortage will need to be prioritised until the supply can restored.
Tom Lewis, a consultant microbiologist at North Devon Healthcare NHS Trust, told Sky News: "The worry we have got locally is we use Roche to provide us with swabs that we use for our COVID testing.
"We are expecting a delivery next week and we don't know if we are going to get that or not. Obviously if we don't get those, that has a massive potential impact on our COVID diagnostics locally."
Roche Diagnostics confirmed COVID-19 testing will also be impacted, but the company says it will prioritise supply of PCR and antibody tests to the NHS.
The pharmaceutical giant said it "apologised" for any delay and its team at the company's national distribution centre are "working night and day to resolve the issue as soon as possible".
In statement, it added: "As well as extending working hours, we have recruited extra staff and, where they can, our dedicated teams on the ground are working with customers to distribute products and minimise service disruption.
"We will continue to provide regular updates to our customers and we are doing everything possible to return to routine operations.
"We are prioritising the dispatch of COVID-19 PCR and antibody tests and doing everything we can to ensure there is no impact on the supply of these to the NHS. Roche pharmaceuticals are not affected."
An NHS spokesman said: "Roche has alerted hospitals to an issue with their supply chain, and they will be working urgently to resolve this issue."
International Trade Secretary Liz Truss told Sky News that Roche was "pushing very hard" to resolve the issue and that her Cabinet colleague Matt Hancock, the health secretary, was being "regularly updated".
"I would encourage people to continue going through the testing process," she added.
"That process is still working."