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 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.