My company's system administrator is asking for our passwords for an ISO audit and my VP IT operations support says it's mandatory for ISMS (ISO27001).

Can someone confirm if this is true?

Absolutely not! 

ISO 27001 requires management of passwords and requires having password policies. Someone in your company is interpreting this as needing to inspect all passwords in the clear to ensure that they meet the password policy. 

But this is a terrible way of doing this audit. Technology should be in place to force people to comply with password policies when they make passwords, not to inspect them by hand once they are made. 

There is a wide-ranging series of failures if they want to audit passwords by looking at them ...
