However, it did not believe it was responsible for the content on third-party websites, such as blogs.
While it would be easy to "surgically" remove offensive material from its own website or services, it would be more difficult to police an external site.
"If the court required us to block specific content on a third party's website that we might be hosting, that would require a level of intervention that's much more like a sledgehammer," Ms Reynolds said.
Asked by MPs to give an example, she said: "Let's just say we hosted a blog like Whale Oil. And if someone complained about material that was on there ... the district court could conceivably come to us and say, 'You host this. Could you please take it down.'
"And the only option for us would be to remove the website entirely."
Vodafone said the committee should amend the legislation to target only the organisations with direct control of harmful material.
The company said it already took its anti-bullying responsibilities seriously with initiatives such as a "blacklist" that allowed people to block mobile numbers.
A number of heavyweight tech and online companies, including Facebook and Microsoft, have made submissions on the cyber-bullying law changes. They are generally supportive of its intentions but want some amendments to ensure that the law does not over-reach.
Facebook head of policy Mia Garlick said that as it stands, the bill could capture comments on social media that were made in poor taste or poor judgement but were not necessarily harmful. She recommended the definition of harmful communication was narrowed and examples were provided for clarity.