The Russian government expects a 0.8% decline in GDP next year, compared with 0.6% GDP growth in 2014 as a whole.
The rouble fell to a rate of 57 to the dollar on Monday, a fall of more than 6%, after some gains last week.
Russia's economy, heavily reliant on energy exports, has been hit by the oil price slump and Western sanctions.
The sanctions, imposed because of Russian support for separatists in eastern Ukraine, target the oil and gas industries as well as banks, arms manufacturers and the wealthy elite close to President Vladimir Putin.
Russia blocked most imported Western food in retaliation for the measures.
The rouble has lost half its value against the dollar this year.
The Russian ministry for economic development said the manufacturing, construction, agriculture and service sectors all contracted in November. Energy, mining and the retail trade showed continued growth.
President Putin signed a law on Monday doubling the deposit guarantee for bank accounts, to 1.4m roubles (Â£16,290; $25,370).
The last time Russia suffered a major economic crisis, in 1998, many ordinary Russians saw their bank savings wiped out.
Mr Putin has also given the Russian central bank the power to recapitalise the country's biggest retail bank, Sberbank, directly with soft loans. The total must not exceed Sberbank's capital as measured on 1 January 2015.
The "subordinated debt" issued by the central bank, if Sberbank needs it, will not have to be repaid until other loans have been paid off. It is a cushion in case Sberbank gets into financial difficulty.
Other banks can be recapitalised by the central bank through Russia's deposit guarantee agency, using federal government bonds.

Fire Brigades Union (FBU) members walked out at 18:00 GMT on Friday and are due back on 4 November.
Some fire brigades have warned the public could be left "vulnerable" and small fires may not be attended.
Fire Minister Penny Mordaunt said fire and rescue authorities have "robust" plans in place for the weekend.
Union officials say that under the government's proposals firefighters will have to work until they are 60 instead of 55, pay more into their pensions and get less in retirement.
The proposals will leave firefighters at risk of dismissal as their fitness declines into their 50s, the FBU said.
FBU members went on strike in England and Wales in August over the same dispute.
Strike action due to take place in Wales has been averted after a "significant" change of direction by the Welsh government, the FBU said.
General secretary Matt Wrack accused the Westminster government of "sickening hypocrisy".
"The real scandal is that their own pensions are by far the most generous anywhere in the public sector," he said.
One firefighter and his son carved pumpkins together and tweeted a photo in support of the strike.
"It's an issue which affects both me and my family and I have explained the dispute to him," said the firefighter, who asked not to be named.
The West Yorkshire brigade said the public would be left in a "vulnerable position" and asked people to take extra care this weekend.
The London brigade said it may not attend rubbish or small grass fires or help anyone stuck in a lift.
Industrial action over the past 18 months has seen fire authorities spend millions hiring contractors to cover for striking FBU members.
The FBU said it expected about 36,000 firefighters to walk out.
The fire minister said: "All fire and rescue authorities have robust and well-tested plans in place that include back-up support if needed.
"Public safety is the primary focus and if anyone needs emergency assistance, they should dial 999."
She said strike action was "unnecessary" after pension regulations laid in parliament on Tuesday mean nearly three quarters of firefighters will see no change in their pension age in 2015.

The blaze took hold of the Royal Victoria Hospital building at about 16:20.
Firefighters used six pumping appliances and breathing apparatus to battle the blaze. They were still at the scene a number of hours later.
A Scottish Fire and Rescue spokeswoman said there were no casualties in the incident.
The fire was reported by a significant number of people as smoke rose from the abandoned building.
The Royal Victoria Hospital was closed in 2012, but later temporarily reopened to deal with seasonal demand.
The Russian economy contracted by 0.5% in November, the first fall in national output - Gross Domestic Product - since October 2009, official figures show.
[NEXT_CONCEPT]
Firefighters across England are on a four-day strike in a row over pensions during one of the service's busiest weekends of the year.
[NEXT_CONCEPT]
A fire at a disused hospital in Edinburgh led to thick smoke being seen across the city.