The victim was shot dead in the underground parking lot of the Frick Bank at around 7.30am, said police from the principality between Switzerland and Austria.
A radio station identified the dead man as the bank's CEO, Swiss newspaper Blick reported online.
National police described the suspect, named in media reports as Jürgen Hermann, as “armed and dangerous”.
He was travelling in a white and grey Smart car with Liechtenstein licence plates.
Police said anyone encountering him should exercise "extreme caution".
Investigators issued a photo of the suspect showing a bald man wearing wire-rim glasses and a tropical shirt.
Hermann, a resident of Mauren, a small town of 3,700, is known in the country for running a fund company that went bankrupt in 2004, according to Swiss media reports.
He blamed the Frick Bank in Balzers and Liechtenstein's former office of financial services for the company’s difficulties, launching a 200-million franc ($225-million) lawsuit against the state, 20 Minuten newspaper reported online.
He took his case to the public by distributing a letter to households across Liechtenstein, casting himself as a “Robin Hood” of the Liechtenstein financial sector, the newspaper said.
However, his claims were rejected.
On his own website, Hermann alleges he was ruined by the Liechtenstein "financial mafia".
A native of Liechtenstein, he spent 18 years in the US, has been married since 1980 and is the father of three children, according to the site.
In addition to being a fund manager, he claims on the site to be a "cleantech visionary" investing in hydrogen and solar power.
He also describes himself as an "engineer, inventor and entrepreneur", with more than 30 international patents, who founded companies in the Silicon Valley, Hawaii and Switzerland.
Anyone with information about the suspect’s whereabouts is asked to phone 423 236 71 11.