Denmark announced that gas was leaking from the parallel Nord Stream 2 pipeline and told mariners to avoid a radius of 9.3 kilometres around the source.
It came shortly after Germany reported pressure drops on Nord Stream 1, which has not delivered gas for weeks, and Nord Stream 2, which has been idle since February.
Danish Prime Minister Mette Frederiksen said it was hard to believe the leaks were a coincidence, while others said it was too early to speculate.
Kremlin spokesman Dmitry Peskov said sabotage on the undersea routes could not be ruled out.
"Breakage of gas pipelines is extremely rare," said Kristoffer Botzauw, the director of Denmark's Energy Agency.
European Commission President Ursula von der Leyen said the leaks in the Nord Stream pipelines were caused by sabotage, and warned of the "strongest possible response" should active European energy infrastructure be attacked.
"Any deliberate disruption of active European energy infrastructure is unacceptable and will lead to the strongest possible response," Ms von der Leyen said.
The US said it was ready to help European allies over the incident.
Secretary of State Antony Blinken said the US was looking at reports that the leaks were "the result of an attack or some kind of sabotage".
"If it is confirmed, that's clearly in no one's interest," Mr Blinken said.
But he said he believed the leaks would not have a significant impact on Europe's energy resilience.
After flying helicopters over the danger zone, Denmark's armed forces released images of the turbulent Baltic waters where gas was leaking.
The boiling seas covered an area of more than a kilometre in diameter near one of the leaks, with a Danish frigate sent to the exclusion zone.
German authorities said they were working to establish the cause of the leak and whether it had occurred in German territorial waters. The two pipelines run across the Baltic Sea from Russia to Germany.
A spokeswoman for Sweden's Maritime Administration told The National that planes were being diverted as well as ships, and were told to maintain a 1,000-metre altitude.
The spokeswoman said there was no information on the cause of the leaks.
Nord Stream’s Russian operators said the pressure drop had been detected late on Monday and was being investigated.
“The only positive thing is that Germany and Europe are no longer dependent on the Nord Stream 1 pipeline,” said Klaus Mueller, the head of Germany’s grid regulator, after a race since February to find alternative sources of energy.
Russia and its state-owned gas exporter Gazprom have blamed technical faults for the cut to deliveries through Nord Stream 1, which slowed over the summer and came to a complete halt this month.
Germany says the technical problems are spurious and accuses Russia of deliberately breaching its contracts.
But the pipeline was still filled with gas and the Kremlin had indicated that it could be put into service if Europe had a change of heart — as a minority of politicians in Germany have demanded.
Denmark’s Energy Agency said Nord Stream 2 was leaking gas south-east of the island of Bornholm.
It said the leak was dangerous for naval traffic because ships could lose buoyancy or the fuel could ignite.
Swedish officials said there were two leaks near each other on Nord Stream 1, one in Swedish and one in Danish waters.
No gas has been delivered through Nord Stream 1 since September 1, after it closed for what Russia described as maintenance.
Germany’s gas tanks have been filled to 91 per cent in preparation for winter.
The Baltic Pipe, a new subsea pipeline delivering Norwegian gas to Poland with an annual capacity of 10 billion cubic metres a year, was inaugurated at a ceremony later on Tuesday.