This is classic conflict of interest, as others have said. Depending on how well organised the company you work for is, there could even be a procedure for how to deal with this, speak to your line manager.
Depending on the terms of your employment contract / the B2B contract / laws in your country you very likely primarily represent your employer and not your client. In the event of a conflict of interest your employer comes first.
EDIT based on comments:
To clarify, this is a conflict of interest between the two companies. There is no conflict of interest for the OP as they will not have any personal material gain by knowing the information, notwithstanding using it to setup their own business and gain a commercial advantage, but this is not an avenue being explored afaik.
Conflicts of interest are likely handled in the contract depending on how organised/large the companies are. There could be a clause on how to handle this.
Businesses do not like surprises, OP could sort this out ASAP buy just being open with the situation. Businesses also do not like having clients that want to leave anyway - if they want to go the best thing to do is let them go - then everyone can move on.
Yes, the company could have idiots but that (sadly) it is not a reason to not inform them.