New Year's revellers were first to the cashpoints
Slovakia has become the 16th member of the eurozone - the second former communist country to join the grouping.
Up to 100,000 people gathered in the capital Bratislava's main square for a midnight ceremony with fireworks.
Slovak Prime Minister Robert Fico was one of the first to withdraw the new currency, taking 100 euros from a cash machine in the parliament building.
The Slovak koruna (crown) will remain in circulation alongside the euro until 16 January.
Cash machines were meant to be issuing euros from Thursday, while some banks planned to open, despite the New Year's Day holiday, to swap korunas for euros.
But the new currency was taking a while to filter through.
"None of my clients has paid with euros yet, everybody's using korunas," Marek, a 30-year-old taxi driver in Bratislava, told the AFP news agency.
At Bratislava's railway station, Richard Nedo, a 20-year-old waiter at an internet cafe, said: "Since we opened at 6am, we have had 10 customers but only three of them - foreign tourists - paid with euros. Slovaks are still using korunas."
Slovakia sees its adoption of the euro as a shield from the turbulence that has hit currencies in neighbouring ex-Soviet bloc countries.
The koruna has been pegged at a rate of 30.126 to the euro since July, while Poland's zloty has lost 24% against the euro, the Czech koruna 11% and the Hungarian forint 13%, Bloomberg news reports.
A recent poll in Slovakia's Hospodarske Noviny daily showed 58% of respondents in favour of the euro, compared with 43% positive a year ago.
Euro "starter packs" have already been distributed in Slovakia and a big campaign has been under way to familiarise the nation of 5.4 million with the new currency.
Slovakia has enjoyed rapid economic growth since joining the European Union in 2004.
But the euro's strength may make life harder for Slovakia's exporters - particularly its big car industry - in the current economic downturn, correspondents say.
The Slovak koruna (right) has been pegged to the euro since July
Slovakia's cabinet is counting on 4.6% economic growth, down from a peak of 10.4% in 2007, Reuters reports.
The small Alpine nation of Slovenia, formerly part of Yugoslavia, was the first ex-communist country to join the euro in its own right, two years ago.
However, the former East Germany - now part of Germany - has been involved in the euro project since the beginning.