Only if you distribute the binary/source of the GPLd library. You may build a non-GPL program that dynamically links with a GPL library and freely distribute it. As long as your program does not contain copyrightable code, you do not have to comply with the licence requirements, because you do not need a licence at all to do that. Same applies for static linking if you only distribute the source and require your users compile the program themselves.
This is not limited to GPL, but applies to proprietary libraries as well. It's OK to require a proprietary library at runtime and you don't need a licence to do that. As long as you do not distribute some intellectual property, copyright law and its limitations are not applicable at all.
This sounds quite assertive, so compulsory "IANAL, this is just my interpretation".