Mr Peake, who is spending six months carrying out scientific experiments in space, tweeted an apology following the incident on Christmas Eve.
He said: “I’d like to apologise to the lady I just called by mistake saying ‘Hello, is this planet Earth?’ – not a prank call ... just a wrong number!”
A former major in the army, Mr Peake is the first Briton to join the crew of the ISS and is employed by the European Space Agency.
The 43-year-old was waved off earlier this month by his wife Rebecca – who is originally from Comrie in Perthshire – and his two sons as he blasted off from the Baikonur Cosmodrome in Kazakhstan.
The astronaut has spent six years preparing for the role, undertaking 6,000 hours of training and spending the two weeks before lift-off in quarantine.
Speaking earlier this month, Mr Peake described the moments after take-off.
He said: “It was a beautiful launch. That first sunrise was absolutely spectacular. We also got the benefit of a moon rise which was beautiful to see.”
Helen Sharman became the first British citizen to travel to space when she visited the Soviet space station Mir in 1991. Other Britons who have flown into space have done so either as private individuals or by taking US citizenship.
Yesterday, people across the UK were expected to get a glimpse of the ISS as it soared 250 miles over the French-Spanish border.
Major Peake and the crew were expected to be treated to a spectacular sight as their orbiting craft flew over the Christmas lights of Europe.
Robin Scagell, vice-president of the Society for Popular Astronomy, said: “The space station’s maximum elevation will be about 23 degrees viewed from London, which is just above the rooftops.
“It will be the brightest star in the sky, moving rapidly from west to east. You might think it’s a plane to start with, but you’d hear the engine noise of an aircraft that close and of course the space station is silent.
“So we’ll be able to see a different object flying over the rooftops on Christmas Day.”
Viewed from further north, the space station appears lower in the sky, but was expected to be visible from the north of Scotland.