Over the past two years, there has been a number of kidnappings of foreign aid workers and journalists in Gaza, usually by groups or families pressing the government for money or job guarantees.
In most cases, the hostages were quickly released and none have been seriously harmed.
The Red Cross said Claudio Moroni and Gianmarco Onorato were abducted in Deir el-Balah in central Gaza after their car was stopped by armed men.
In the northern Gaza Strip, Palestinians said on Wednesday a member of Hamas' security personnel had been killed by Israeli tank fire.
The Israeli army said it fired at a group of armed men who were laying explosive charges in the path of soldiers operating in the area.
Israel has killed more than 370 Palestinians in Gaza since it began the offensive, hospital officials and residents say.
Iyad Nasr, a spokesman for the Red Cross's Gaza office, said the organisation had ceased all field operations and would intervene only "in matters of life and death".
Workers have been ordered to stay in their offices because of fears for their safety, he said.