The company said it was removing the logo - a white Z on a blue background - because it did not want to be misinterpreted as supporting Russia in the conflict.
In a statement, the company said: 'We are temporarily removing the use of the letter 'Z' from social channels where it appears in isolation and could be misinterpreted.
The company also told the Telegraph: 'The Zurich brand has been around for 150 years. It is a trusted brand and we have proven our ability to change and respond to challenges over time.'
It comes after Zurich Insurance said earlier this month that it was no longer taking on new domestic customers in Russia and will not renew existing local business.
The company is one of Europe's biggest insurers and has a market cap of $66.bn ($50.4bn).
The letter Z has been used to mark Russian military vehicles in the Ukraine conflict.
It has also appeared on buildings, roads, cars, t-shirts and flags in Russia as a sign of support for the war.
Russian politician Maria Butina, who was convicted in the US in 2018 for acting as a foreign agent, posted a picture of her and her colleagues in Z t-shirts earlier this month.
She captioned the photograph: 'The team in support of our army and president! Let's get to work guys!'
And politician Mikhail Delyagin wore a badge in a meeting of the state duma or parliament emblazoned with a 'Z'.
In the meeting, the government approved Draconian new laws.
Mr Delyagin said in a statement: 'Now we are at war. Yes we have a special operation in Ukraine, but we have a war with the West.'
Also, children from a Russian cancer charity lined up in a giant 'Z' with their mothers earlier this month to show support for the invasion of Ukraine.
And in the Gymnastic World Cup in Doha, Russian athlete Ivan Kuliak wore a 'Z' at the medal ceremony, prompting widespread outrage.
There have also been videos of Russians wearing black sweatshirts with a white Z on social media to show their support for Putin's invasion of Ukraine.