The French firm has announced plans to sell investments worth more than €1.7bn (£1.4bn), the Financial Times reports.
The company’s incoming chief exec Thomas Buberl said the move was intended to support the efforts of governments around the world to stamp out smoking.
"This decision has a cost for us but the case for divestment is clear: the human cost of tobacco is tragic, the economic cost is huge," he said.
Axa says the decision to divest makes it the first commercial insurer to make a stand on tobacco - although publicly connected bodies, such as the Norwegian oil fund, and US pension groups Calpers and Calstrs, have already done so.
Alice Steenland, head of corporate responsibility, said: "We are aware of the past performance of tobacco investments. This is a decision we are proud to make. It is a sunset industry. More and more countries are going to put controls on it."
These controls are likely to include plain packaging, which has now been introduced in the UK. From last Friday, all tobacco packs manufactured for sale in the UK must be the same dull green colour – "Pantone 448 C opaque couché" – with brand names printed in the same font, and health warnings covering at least 60% of the pack.
Axa’s home country, France, has introduced similar legislation.
Axa’s move comes exactly a year after it said it would sell of more than €500m in coal investments, just before the Paris climate change summit.