Not enough information to provide a useful answer. In fact, even if you provided more information, it would probably still be necessary to profile, and benchmark alternatives.

Minimally, we would need to know a lot more about the design; will the objects have methods called on them which are currently handled by plain old subroutines? What object framework will you use. Have you determined (before making the switch) where performance bottlenecks are most significant in your existing code?

Converting a script that passes references to hashes as parameters to subroutines, into a script that calls object methods on objects that hold references to hashes will have some non-zero performance impact. The impact doesn't come from the fact that there's a blessed hash involved, but rather, that method calls have to go through a layer of lookups to decide what method to invoke out of the inheritance chain. But anyone who is eager to quantify the impact without methodical testing, profiling and benchmarking is just guessing.