Researchers have found such calls can be as distracting as with handheld mobiles and road safety groups have advised drivers against the practice,
The online advert showed the man calling an assistant to request her to complete an urgent task ahead of a trade show to which he was travelling. It had run on various websites since last week.
After being contacted by the paper, Vodafone said it had pulled the advert and would alter it to remove the sections showing the hands-free call.
The firm said it acted because it advised both its own staff and customers not to make phone calls at the wheel. However, it said it was unable to provide a copy of the advert or images from it.
A spokeswoman said: “Thank you for letting us know about this. We advise our own employees and our customers when driving to stop their vehicle safely and switch off the engine if they need to make or take a call, or let the call go to voicemail.
“While it is legal to use a hands-free phone, we would strongly recommend keeping a call extremely short, and only use the mobile phone if it is absolutely necessary.
“We have adjusted our ad to better reflect our company-wide position.”
Road safety group Brake, which this week launched a campaign urging motorists to put their phones in the glove box while driving, welcomed the decision.
Campaigns director Jason Wakeford said: “Countless studies have proven that using a mobile phone when driving is incredibly distracting, even hands-free kits – increasing the chance of being involved in a deadly crash.
“Mobile phone operators simply must set a good example of safe driving behaviour.
“We’re glad to hear that Vodaphone is to now amend its ad accordingly.”
Such research includes a Sussex University study last year which found that drivers failed to see hazards and focused on a smaller area of the road when on even hands-free calls.
This is because more of their visual processing capacity than previously thought is used to visually imagine what they are talking about.
Fatal incidents include a seven-year-old boy being hit by a driver using her mobile’s loudspeaker function in Lincolnshire three years ago.
Philip Gomm, of the RAC Foundation, said: “Given a third of people hurt on the roads each year are on company business, Vodafone is right to go beyond the strict letter of the law and promote what is best practice when driving – ignore the phone whether you have to pick it up or not.”
However, AA president Edmund King said: “Sometimes a short, sharp hands-free call via voice activation can enhance safety. For someone stuck in traffic en route to a meeting, rather than panic, speed or commit road rage, a quick call to say they will be late releases tension.”