Tension heats up between Puntland and Somaliland
She said the move was due to possible contact between Al-Qaeda militants based in Yemen, who are accused of being behind the plot, and "terrorist" groups based in Somalia.
The government banned all freight from Yemen from coming into the country, including in transit, shortly after the discovery of one of the bombs at an airport on Friday. Another package was found in Dubai.
"From midnight tonight we will extend the suspension of unaccompanied air freight to this country not just from Yemen but also Somalia," May told parliament.
"This decision has been made as a precautionary measure and it will be reviewed in the coming weeks," she added following a meeting of the COBRA emergency committee.
"It is based on possible contact between Al-Qaeda in Yemen and terrorist groups in Somalia, as well as concerns about airport security in Mogadishu."
May said the government would also ban passengers from carrying toner cartridges larger than 500 grammes in their hand luggage for an initial period of one month.
Toner cartridges would also be banned from air cargo unless they come from a "regular shipper" with security arrangements approved by the transport ministry.
The two bombs found contained 300 and 400 grammes of the high explosive PETN hidden inside toner cartridges, a German government official said in Berlin.
If they had gone off, "they would have caused significant damage," the official said, without specifying the source of the information.
May said that during the next month the government would "work closely with the aviation industry screening equipment manufacturers and others to devise a sustainable, proportionate long-term security regime to address the threat."
Prime Minister David Cameron, who chaired the COBRA meeting, vowed earlier Monday to "cut out the terrorist cancer" from Yemen and the surrounding region following the plot.
"The fact that the device was being carried from Yemen to the UAE to Germany to Britain en route to America shows the interest of the whole world in coming together to deal with this," Cameron said.
"While we are rightly engaged in Afghanistan to deny the terrorists there, the threat from the Arabian Peninsula and from Yemen in particular has grown."
The prime minister added: "It is clear that we must take every possible step to work with our partners in the Arab world to cut out the terrorist cancer that lurks in the Arabian Peninsula."
The two regional states have been at loggerheads over the control of the Sool and Sanaag regions which are located on their border.