The insurance sector provides protection to individuals and businesses against many types of risks and also promotes economic growth, being an important source of long-term capital. Analyzing factors that facilitate insurance sector development is important for both individuals and the entire economy. The purpose of this study is to investigate the relationship between information and communication technologies (ICT) represented by mobile cellular subscriptions per 100 people and individuals using the Internet (% of population) and insurance sector development represented by insurance company assets to GDP (%). Using data from 10 new member states of the European Union for the period 2000–2020, this study reveals a mutual interaction between ICT penetration indicators and insurance sector development. Furthermore, a regression analysis reveals that Internet penetration has a significant positive influence on insurance sector growth. Specifically, at the country level, the results indicate the existence of bidirectional causality between mobile cellular subscriptions and the insurance sector in Latvia, Poland, and Slovakia, and unidirectional causality between insurance and mobile cellular subscriptions in Estonia and Hungary.