Shares in BT initially dropped nearly 4% and TalkTalk put the sale of one of its businesses on hold after the Labour Party announced plans to turn broadband into a public service
Jeremy Corbyn is due to officially announce the new policy in a speech in Lancaster on Friday morning.
Labour has costed the policy at £20 billion, saying it will deliver free full-fibre internet to every home and business by 2030 if it wins the General Election.
But BT chief executive Philip Jansen said the Labour Party had dramatically under-estimated the price of its pledge, saying it would cost closer to £100 billion.
Speaking on BBC Radio 4's Today programme, he said: "You've got a big capital investment, say £30 to £40 billion, if you're giving it away free, for example, that's probably another £5 billion a year of revenue that Open Reach currently gets in from its customers.
"So, you've got that big investment to make and I guess, from my perspective, what's really important to me is my employees, our colleagues at BT at Open Reach, our shareholders and our pensioners.
"Remember, the BT group has over 100,000 people working every single day.
"We also have hundreds of thousands of people who used to work for BT who have pensions that they rely on, and we've got to make sure we're generating the returns for those pensioners, and also very, very importantly, for our shareholders, because ultimately they currently own the company.
"So, all I'm really saying is these are very, very ambitious ideas, and the Conservative Party have their own ambitious idea for full-fibre for everybody by 2025.
"How we do it is not straightforward, it needs funding, it's very big numbers, so you know we're talking £30 to £40 billion per building, and if you're giving it away it's again a sort of eight-year timeframe, it's sort of another £30 to £40 billion. So you're not short of £100 billion."
Asked whether it would be owned by the Government or the state or public sector, Mr Jansen added: "The mechanism for that is not straightforward as we have a liability to our pensioners which we see as a responsibility of £60 billion."
On criticism that a lot of money people pay goes out in the form of dividends to shareholders, he said: "Our shareholders ultimately own the company and they provide the investment into the infrastructure, and ultimately, as you probably know, our share price has gone backwards significantly.
"I think we were £5 not long ago and now we're down to sort of around £2. It's had a major knockback.
"So, shareholders are nursing massive losses on their investments should they have bought in at £5, say, two years ago – that's market forces."
The BT share price later stabilised to just a 2% fall – nevertheless wiping nearly £500 million off the company's value.
Meanwhile TalkTalk's chief executive Tristia Harrison told the PA news agency the sale of its full fibre broadband business, FibreNation, has been put on hold after the Labour announcement.
And James Lusher, Virgin Media's head of external communications, made his views on Labour's policy clear by tweeting a gif of a raccoon stealing food from a cat bowl captioned with the words: "This mine now."
Labour has said the pledge will be paid for through the party's Green Transformation fund and taxing corporations such as Amazon, Facebook and Google – adding it will save the average person £30.30 a month.
They said there would be a one-off capital cost to roll out the full-fibre network of £15.3 billion, in addition to the Government's existing and not yet spent £5 billion commitment.
The rollout would begin with communities that have the worst broadband access, including rural and remote communities and some inner city-areas, followed by towns and smaller centres, then by areas currently well served by superfast or ultrafast broadband.
In a speech on Friday, Mr Corbyn will say the internet has become such a central part of our lives, adding: "That's why full-fibre broadband must be a public service, bringing communities together, with equal access, in an inclusive and connected society.
"It's time to make the very fastest full-fibre broadband free to everybody, in every home in every corner of our country."
One of the goals is to deliver the service to at least 15-18 million premises within five years.
Julian David, chief executive of tech trade association techUK, said: "These proposals would be a disaster for the telecoms sector and the customers that it serves.
"Renationalisation would immediately halt the investment being driven not just by BT but the growing number of new and innovative companies that compete with BT.
Nicky Morgan, Secretary of State for Digital, Culture, Media and Sport, said: "Jeremy Corbyn's fantasy plan to effectively nationalise broadband would cost hardworking taxpayers tens of billions.
"Corbyn is clearly so desperate to distract from his party's divisions on Brexit and immigration that he will promise anything, regardless of the cost to taxpayers and whether it can actually be delivered. What reckless idea will be next?"