David Lockwood said the timescales around any future independence negotiations mean such a move would be “manageable”, though not ideal.
The same site assembled the Queen Elizabeth-class aircraft carriers.
However SNP MP Stewart McDonald responded to Mr Lockwood’s concerns by saying the Rosyth yard would be “not just welcome, but vital” in an independent Scotland.
Asked about a second independence referendum, Mr Lockwood told The Courier: “I lived in Scotland for 10 years and it was a rumbling thing then and I think it’s just going to be a rumbling thing.
“I think in reality there will be plenty of warning if the vote were in favour of independence.
“There would then be a negotiation period and at the end of the negotiation period there would be an implementation period.
“I don’t think there is anything that we can’t manage as a company.
“When you look at the timelines, there’s nothing we can’t manage as a company.
“If we had to replicate this in England because we were told we weren’t welcome here – which I think would be a bad mistake for Scotland – but if that were the decision, we can replicate this in three years, and the time window of negotiations is longer than that.
“It’s not ideal but it is manageable.”
Mr McDonald responded saying: “Important to note independence described as ‘manageable’ for Babcock, but would only leave if ‘made to feel unwelcome.’
“Babcock is not just an important employer, but would play a crucial role in an independent Scotland’s defence capability. Not just welcome, but vital.
“Scotland’s defence industry is a well established part of our economy, and it’s vital that we can show that the future of that industry has a place here with independence.
“It’s not just the right thing to do for peoples jobs, but for our own defence and security posture too.”