Norway and Denmark say they will open up tourism between their two countries from 15 June but will maintain restrictions for Swedes.
Sweden did not impose a lockdown, unlike its Nordic neighbours, and its Covid-19 death toll - above 4,000 - is by far the highest in Scandinavia.
Danish PM Mette Frederiksen said Denmark and Sweden were in different places regarding the pandemic.
Denmark is also opening up tourism with Germany and Iceland, within limits.
Tourists from those countries cannot stay the night in Copenhagen, which has the most coronavirus cases. Danes can travel to those two countries too, without having to go into quarantine on their return.
The announcement dashes the hopes of Danes hoping to travel to Southern Europe for their holidays and Denmark's foreign minister said they should avoid big cities and stick to the countryside.
At a joint video news conference, Norwegian Prime Minister Erna Solberg said "we can't open too suddenly, that would jeopardise everything we've accomplished".
Danish-Swedish economic ties are very close, especially in the Oeresund region, where they are linked by a giant suspension bridge. Moreover, they are both in the EU, whereas Norway is not.
Sweden's 10 million population is also bigger than that of Denmark (5.8 million) or Norway (5.4 million).
Denmark still cautious
Foreign Minister Jeppe Kofod said "we can start gently opening up journeys from Denmark to a small group of neighbouring countries where the infection with Covid-19 is considered to be best under control".
He advised Danish tourists to avoid urban areas with 750,000 inhabitants or more.
"We will still advise against all unnecessary trips to the rest of the world until 31 August," he said.
Swedish Foreign Minister Ann Linde warned earlier this week that excluding Sweden from moves to open borders across the Nordic region would be a political decision and not justifiable on health grounds.
In comments reported by Swedish TV on Friday, she said Sweden had hoped for a common Nordic solution but it was impossible.
The three Baltic states - Estonia, Latvia and Lithuania - were the first in the EU to create a "travel bubble" enabling free cross-border movement for their citizens during the coronavirus crisis.
Prime Minister Frederiksen said she was continuing to negotiate with the Swedish government and hoped for a regional border solution for the Oeresund region.
What about tourism elsewhere in Europe?
- Greece says it will start reopening its airports to tourists from 29 countries from 15 June. They include 16 EU countries, but not countries hit hardest by Covid-19: the UK, France, Spain and Italy
- Spain says that from 1 July tourists will be allowed in without having to spend 14 days in quarantine
- Italy plans to allow in tourists from EU countries from 3 June, when mandatory quarantine for visitors will be lifted
- France plans to reopen borders from 15 June, initially to tourists from Switzerland and Germany
- Switzerland plans to reopen its borders with France, Germany and Austria on 15 June, but not with Italy
- Cyprus plans to reopen its airports on 9 June to a number of countries seen as low risk, including Germany, Greece, Israel and Malta, but the UK and Russia are not among them
- On 28 May Croatia reopened its borders without restrictions to citizens from 10 EU countries seen as low risk, including Germany, Austria, the Czech Republic and Poland.