Jalalabad is near the Pakistan border
Ms Ridley - who is 43 and works for the Sunday Express - is said to have been detained on Friday near the eastern city of Jalalabad, for allegedly entering the country illegally.
International journalists' organisation Reporters Without Borders has written to Afghan foreign minister Wakil Ahmed Muttawakil urging the release of Ms Ridley.
The Afghan Islamic Press said Ms Ridley was arrested with two guides, was wearing traditional Afghan dress and was not carrying any travel documents.
'Treat her well'
A spokeswoman for the Foreign Office said: "We are making inquiries about her well-being and any charges that may be brought against her.
"If these reports are confirmed we urge those holding her to treat her well and to resolve this situation quickly."
Afghanistan has expelled foreign journalists and refused to issue new visas.
Rebekah Wade, News of the World editor and chair of Women in Journalism, said she had written to UK Foreign Secretary Jack Straw urging him to do everything in his power to secure Ms Ridley's safe release.
Ms Wade said: "Yvonne Ridley is a brave reporter who is just doing her job and we feel sure that she will not have meant to offend the Taleban regime in any way.
"We hope that all efforts are made to secure her safe release.
"Women in Journalism has offered any funds that they may have to Yvonne Ridley should legal proceedings become necessary."
'Offensive regime'
Ms Ridley's father Alan Ridley broke down in tears as he spoke to reporters gathered outside his home in County Durham.
He said his eight-year-old granddaughter Daisy had yet to be told of her mother's arrest.
"She knows how much we love her and we just want her home."
Mrs Ridley's former husband Daoud Zaaroura, chief executive of the Northern England Refugee Service, described her as "a journalist of great integrity and courage who shows no fear in pursuit of a story".
"She is in the hands of a regime that is very offensive and it's very difficult to predict what might happen," he said.
'Deep concern'
Ms Ridley is understood to have been in the Middle East since the US atrocities two weeks ago.
She had been reporting for both the Sunday Express and Daily Express from Peshawar and Islamabad in Pakistan.
A spokesperson for the Sunday Express said Ms Ridley was the paper's chief reporter and was "a highly experienced journalist who has worked in many countries around the world.
"Everyone at Northern and Shell and Express Newspapers is deeply concerned and anxious for her speedy and safe return," the spokesperson added.
A former colleague of Ms Ridley told BBC News Online she was not known for taking unnecessary risks.
"She was very knowledgeable, well travelled, had been around the world and was as tenacious as most journalists are.
"She was not the sort of person to take risks but was as hungry as most journalists are to get stories."
Ms Ridley, originally from Stanley, County Durham, is a former assistant editor of the Sunday Sun and former deputy editor of Wales on Sunday.