The new law, first announced in February, prohibits the importation, production, sale and use of plastic bags, which usually end up dumped as litter or buried in landfills.
Environmental campaigners and residents of the capital Mogadishu welcomed the ban, saying it was long overdue.
"This is timely and a very good decision by the government," said Mohamed Gure, who lives near the capital's main Bakara market.
Environmental activist Osman Yusuf said the country was hugely dependent on the plastics bags, saying the industry was worth more than $50 million.
"There is no justification left for people to continue using this deadly material," Yusuf said.
But others worried about a lack of environmentally friendly alternatives.
"We have no problem banning them, but we need time and replacement," said Lul Mohamed, a shopkeeper.
Somalia joins other African countries, including neighbouring Kenya and Tanzania, that have banned single-use plastic bags.
Kenya introduced one of the world's toughest bans on plastic bags in 2017, mandating a fine or even prison terms for using one.
The United Nations Environment Programme (UNEP) estimates that the equivalent of 2,000 garbage trucks of plastic is dumped into the seas, rivers and lakes every day.
Each year 19-23 million tonnes of plastic waste leaks into the world's water ecosystems, UNEP says.
Somalia's ban comes into effect as negotiators concluded a meeting in Nairobi on Monday hoping to reach the world's first treaty on plastic pollution.
The treaty aims to marshal an international response to the plastic trash threatening the environment, from oceans and rivers to mountains and sea ice, and moving up food webs as it is ingested by animals.
Countries are under pressure to find common ground before final negotiations are held in December in South Korea.
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