The British embassy said they were investigating the reported kidnap.
The last foreigner to be kidnapped in
The AFP photographer was released unharmed after nearly one week in captivity.
Johnston has been working with the BBC in Gaza for three years [File photo]
Most news organisations have pulled their staff out of Gaza in recent years, as violence between rival factions has spiralled and crime and lawlessness has increased.
A Peruvian photographer was kidnapped in January and held for a week, while in October a photographer for the Associated Press was held for 15 hours.
The BBC described Johnston as a "highly experienced and respected reporter".
"It is his job to bring us day after day reports of the Palestinian predicament in the Gaza Strip," said the BBC's diplomatic correspondent, Paul Adams, himself a former Middle East reporter.
Alan Johnston was born in Tanzania and educated in Scotland. He joined the BBC World Service in 1991 and has spent eight of the last 16 years as a correspondent, including periods in Uzbekistan and Afghanistan.
He became Gaza correspondent in April 2004 and his posting was due to come to an end at the end of next month.