The country, which lies between Switzerland and Austria, has a population of about 41,000.
The government said it had convened a crisis team led by Prime Minister Brigitte Haas and Justice Minister Emanuel Schädler.
The attack had breached the protection of personal data, it said.
The target was the "register of beneficial owners," a database containing the names and other details of the de-facto owners of companies, foundations or trusts.
The government said it maintains this register to prevent money laundering and the financing of terrorism.
The principality is one of the richest countries in the world measured by gross domestic product per capita.
At just 160 square kilometres, it is also one of the smallest.
Financial and banking services are among its most profitable industries.
Many years ago, Europeans in particular exploited foundations and accounts there for tax evasion purposes.
However, banking secrecy in tax matters was abolished in 2017.
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