Sir Charlie Mayfield said a Brexit would also hit consumer confidence and spending for as long as five years.
Leave campaigners have previously said that the UK economy would thrive outside the EU.
John Lewis was not taking sides in the EU referendum debate, Sir Charlie added.
He said that the UK economy would be stronger if Britain decided to remain in the union.
"As a businessman and looking at the economic issues, I do think that the economy will remain stronger if we remain in the European Union and that does matter. It matters to things like jobs, wages and public services because they do depend on how the economy is performing," he told BBC Radio 4's World at One.
As well as the department store chain, John Lewis also owns Waitrose supermarkets.
Sir Charlie said there were already signs of declining consumer confidence ahead of the 23 June vote.
"From conversations I've had with a number of the banks, we're seeing activity slowing in the build-up to the referendum, so I do think that it's the case that this is beginning to have an impact on the economy," he said.
"We're not taking sides in the debate. It is up to people to decide. But equally we have been asked to decide by our partners - that's 90,000 people who work in our business - what this means for their business because understandably they're interested."
John Lewis has told staff that a vote to leave the EU would have an "adverse impact" on consumer confidence and activity.
"It's very, very hard to say how long that would last, but we estimate it could be for a period of maybe five years," Sir Charlie said. "For example, you have things like a weaker currency. It will probably mean that prices rise. If there is less investment - which seems possible - then that could have an impact on jobs."
However, Vote Leave campaigners have previously said the UK economy would be "turbocharged" outside the EU, with the UK able to form new trade deals with countries outside Europe.
Campaigners argue that the EU sells far more into the UK than the UK sells in the EU, so it would be in the interests of other EU countries to strike a free-trade agreement with the UK after a Brexit.
In March John Lewis and Waitrose staff were told their annual bonuses would be cut for the third consecutive year to 10% of their annual salary.
Higher pension charges and lower property profits resulted in a fall in pre-tax profits before exceptional items from Â£343m to to Â£305.5m for the year to 30 January.
Sir Charlie is also chairman of the British Retail Consortium. It issued a report in February warning that up to 900,000 jobs could be lost from the retail sector, along with the the closure of thousands of shops, over the next decade.
The report blamed rising costs due to the introduction of the National Living Wage and the new apprenticeship levy for the job losses.
UK retail sales rose by 1.3% in April - better than a revised fall of 0.5% in March - despite lower spring clothing sales due to the cold weather, the Office For National Statistics said.

At least 22 staff and patients were killed in the bombing in the city of Kunduz a week ago.
The US has said the strike was a mistake and that it was trying to target Taliban insurgents.
MSF has called the attack a war crime and called for an international committee to investigate.
Those injured in the strike and the families of those killed are eligible for "condolence payments" from the US.
"The Department of Defence believes it is important to address the consequences of the tragic incident at the MSF hospital,"  a Pentagon spokesman said.
Funds will also be made available to repair the hospital, the Pentagon added.
President Obama has apologised to the MSF president and the Afghan leader for the incident.
MSF is still trying to trace more than 30 staff and patients who remain unaccounted for.
Leaving the European Union would probably lead to higher prices in UK shops, the John Lewis chairman has said.
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The Pentagon is to pay compensation for those killed and injured in a US strike on a Medecins Sans Frontieres (MSF) hospital in northern Afghanistan.