A Moscow court ruled Golos had failed to declare itself as a "foreign agent" after receiving funds from abroad after the law took effect in November.
It was fined the sum of 300,000 roubles (Â£6,200; $9,500; 6,300 euros).
The NGO said it had returned the money - a prize for its human rights work - as soon as it entered its account.
It also denied being involved in political activity.
It says it will appeal against the verdict.
Golos, which received assistance in the past from the US government development agency USAID, insists it no longer accepts foreign funding.
By Daniel SandfordBBC News, Moscow
When Golos became the first Russian NGO to be fined under the controversial "foreign agent" law, nobody was very surprised.
From the start many in the Russian opposition felt that Golos was the main target of the law. The NGO's election monitoring in the last two years has caused huge embarrassment to the government, as they exposed the huge level of electoral fraud in Russia.
The organisation always admitted receiving funding from the US and the EU but when the new law came in, saying that any organisation involved in politics that received foreign funding should register as a "foreign agent", Golos said it had walked away from its foreign funding.
Even after today's judgment Golos insisted it was not involved in political activities and it did not receive money from overseas.
Now in its 13th year, the NGO did much to expose fraud at the 2011 parliamentary election, when it charted abuses across Russia, notably through its online "map of violations".
The accusation concerned a sum of 7,728.4 euros awarded by the Norwegian Helsinki Committee as part of its Andrei Sakharov Freedom prize.
Golos says the money entered one of its accounts in December before it had time to decline it, and the sum was later returned unused.
It accused the Russian justice ministry of "rushing to conclusions".
"The Golos association receives no foreign funding and is funded solely by Russian resources," it said in a recent statement.
Under the new law, NGOs involved in political activity which are funded from abroad must register as "foreign agents".
Presenting the case on Thursday, the justice ministry's representative did not specify what political activity Golos was suspected of conducting, the Russian news website lenta.ru reports.
"We are convinced of our innocence," Golos said before the verdict. "This is the first court hearing bringing to responsibility an organisation that is purportedly a foreign agent. The fate of many other NGOs will depend on the decision."
Tax inspectors have been scrutinising the finances of other Russian NGOs in recent months.
USAID was expelled from Russia in September after being accused of attempting to "influence political processes through its grants", which had totalled $3bn.
Election watchdog Golos has become the first non-governmental organisation (NGO) to be fined in Russia under a controversial new law.