The price fell below 4.8 euros in early trading, before recovering to above 5 euros by late afternoon.
Carbon permits are a mechanism designed to reduce carbon dioxide emissions, as companies have to pay to emit C02.
A sharp drop in demand for energy has led to a massive oversupply of permits.
Critics of  the EU's Emissions Trading System also argue that the European Union issued too many permits in the first place.
The EU has proposed freezing up to 900 million permits to tackle this oversupply.
"There are too many permits because of the recession," said Isaac Valero, spokesman for EU Climate Commissioner Connie Hedegaard.
The price of carbon recovered slightly on Monday after demand for an auction of 3.5 million permits was stronger than expected.
A weak carbon price undermines efforts to reduce C02 emissions.
The price of carbon needs to be a good deal higher than 5 euros - some believe between 25 and 30 euros - to provide an adequate incentive for companies to cut emissions and invest in cleaner technologies, experts say.
The carbon market is central to Europe's efforts to meet its climate change target of a 20% reduction in C02 emissions from 1990 levels by 2020.

The Duchess of Cambridge gave birth to a son on Monday afternoon in London's St Mary's Hospital.
The mint in Llantrisant, Rhondda Cynon Taf, announced earlier this month that children who shared the birthday would be able to receive one of the coins.
It has struck 2,013 of the coins. Parents wishing to claim one need to register on the Mint's Facebook page.
Shane Bissett, director of commemorative coin at the Royal Mint said coins had been used to celebrate special events for over 1,000 years.
"We're honoured to be able to mark this momentous occasion in our own way, which is in keeping with an age-old tradition to mark a new birth with a gift of silver for good luck," he said.
"We send our very best wishes to their Royal Highnesses The Duke and Duchess of Cambridge and extend this to new parents across the country today as they celebrate their own special arrivals."
The coins are worth Â£28 each.
In order to claim, parents need to visit Facebook.com/theroyalmint and register their child's birth within 60 days. They will also need to provide their child's birth certificate.

Moeen, 27, took 19 wickets in five Tests against India in 2014 but was less impressive in last week's win over West Indies, despite figures of 4-98.
"India didn't show me enough respect in the way they batted against me," he said. "It's going to be tougher playing New Zealand and Australia."
England start five Tests against the Kiwis in May and Australia in July.
In less than a year since making his Test debut against Sri Lanka, Worcestershire's Moeen has become key to England's attack and was flown out to Grenada for the victory over West Indies in the second Test after recovering from a side strain.
The off-spinner says that decision by the selectors gave him confidence and, despite a slow start with first innings figures of 1-47 then took three tail-end wickets as England bowled the hosts out for 307 in their second innings.
"Even when I wasn't bowling so well in the first innings it gave me confidence the management backed me, liked the way I bowl and think I'm a threat to the batsmen," added Moeen, who averages 27.53 with the ball in his eight Tests.
After a century in his second Test outing, Moeen has not contributed more than 40 in any knock since and is seen as an option to bat at six, with Jos Butler and Ben Stokes also possibilities.
"Whatever the captain and coach want me to bat I'm more than happy," he said. "We see it as a strong batting line up. Hopefully when we all play games and click we can be dangerous."
England begin their final Test of their tour of West Indies on 1 May, leading 1-0 in the series.
The price of carbon hit a record low in Europe on Monday as the over-supply of emissions permits during the global economic downturn continued to undermine the carbon market.
[NEXT_CONCEPT]
Babies born on the same day as the new prince are to receive a silver penny made by the Royal Mint.
[NEXT_CONCEPT]
England spinner Moeen Ali expects his second summer of Test cricket to prove more difficult than his first.