In Italy, the paper said it had not heard from Mastrogiacomo since Sunday.
The reporter had been on assignment in Kandahar, the Taliban's former stronghold in southern Afghanistan, editor-in-chief Ezio Mauro said, according to La Repubblica's Web site.
Massimo D'Alema, the Italian foreign minister said on Italy's Tg1 television news on Tuesday that officials did not believe Mastrogiacomo was "in the hands of a bunch of stragglers, but was effectively captured by the Taliban's military structure".
The ministry and the Italian Embassy in Kabul were trying to find the reporter.
Ahmadi said the journalist had been captured on Monday along with two Afghans as they traveled together by vehicle in Nad Ali district of Helmand province.
"Taliban higher authorities" will decide what to do with them, Ahmadi said: "We are investigating whether they are British spies."
He identified the Afghans as Sayed Agha and Ajmal, giving only one name for the second Afghan.
Ahmadi said the captured reporter had introduced himself as a Briton who had worked for La Repubblica in the Pakistani city of Peshawar, but had been living with British forces in Helmand and gathering information for them.
The British Foreign Office said later on Tuesday it appeared unlikely the missing journalist was one of its nationals.
La Repubblica newspaper said Mastrogiacomo, 52, was born in Karachi, Pakistan, where his father was an engineer for an Italian company.
He has dual Italian-Swiss citizenship, but was traveling only with his Italian passport, the paper said.
Mastrogiacomo, who speaks English, has worked since 2002 as a staff correspondent in Afghanistan, Iran, Israel, Gaza, Lebanon and Iraq.
The Committee to Protect Journalists said it was "greatly concerned about the welfare of our colleague Daniele Mastrogiacomo, who was doing his job documenting the news".
"We call on those holding any members of the press to release them unharmed immediately," Joel Simon, the CPJ Executive Director, said in a statement issued in New York.
Afghan officials said they had no information on the alleged kidnapping.
Most of the NATO-led troops in Helmand are British, and the alliance on Tuesday launched largest offensive to date against fighters in the northern part of the province, a Taliban stronghold.