The BSE - formerly known as Bombay Stock Exchange - asked market entities to take measures to mitigate the threat.
Yesterday, National Stock Exchange (NSE) issued a similar alert against the malicious software script.
Recently, a slew of dreaded ransomware attacks like WannaCry and Petya have impacted the computer systems worldwide.
The alert follows a communique from National Cyber Security Coordinator regarding a highly suspicious communication being observed on the internet in the country.
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"The software infects devices to get foothold in the ICT networks/systems, steals information, passwords and passes over to the adversaries outside the country," BSE said in a circular.
According to the exchange, the software script has the capability to encrypt entire information on the computer system. In some cases, the data hosted or stored on the computer terminals may be lost permanently.
"The infected files reappear again and again. The software script connects to a malicious domain, the location of which keeps on changing in Germany and Russia," it added.
It also advised users to refrain from clicking on suspicious emails and regularly update the security patches on their PCs. Besides, antivirus updates need to be pushed to all end-users and servers.
The bourse advised organisations to "audit their ICT network and systems with respect to the upgrades and updates of anti-virus, operating system and other software and apply upgrades and updates immediately".
Last month, BSE and NSE had asked trading members to take urgent steps to safeguard their systems from Petya ransomware, which has impacted companies across the globe.