Eurostat, the EU's official statistics agency, said eurozone average inflation reached 3.4 percent on an annualized basis, with energy prices increasing by a whopping 17.4 percent.
Inflation in Estonia rose to 6.4 percent in September. This compares to 4.6 percent in Latvia, 6.3 percent in Lithuania and 2.1 percent in Finland.
The rise in costs was far above the 2.0 percent target set by the European Central Bank and will raise pressure on EU governments to take measures to ease the energy cost burden.
Energy is expected to have the highest annual rate in September - 17.4 percent, compared with 15.4 percent in August.
This is followed by non-energy industrial goods - 2.1 percent, compared with 2.6 percent in August; food, alcohol and tobacco - 2.1 percent, compared with 2.0 percent in August; and services - 1.7 percent, compared with 1.1 percent in August.
ECB President Christine Lagarde insists high inflation remains a temporary phenomenon linked to the coronavirus pandemic that has upset supply chains and disrupted the energy market.
Energy prices are becoming a political flashpoint in Europe, with countries considering a wide range of emergency plans to lower the prices for consumers.
Brussels is preparing a series of short-term measures such as cutting value-added tax and excises on energy, in hopes of preserving commitments for more renewable energy sources.