Mr Shaw suffered a black eye, bloody nose and lacerations to his face after being grabbed and hit in the face on Glenmore Street near the Botanic Gardens in Wellington.
National Party deputy leader Paula Bennett told Morning Report the attack was "horrible to hear about".
"You can't even fathom that you're going about your normal morning, walking to work, and then having a completely unprovoked attack like that must have been terrifying," Ms Bennett said.
"It's one of those where politicians and the country unite in being shocked and angry that in this peaceful, beautiful country, we've got this happening to anyone."
However, it was important for MPs to be able to go about their daily lives without security guards watching over them, they said.
Ms Bradford said she faced verbal abuse and death threats over her anti-smacking bill, which was passed in 2007, and was protected by parliamentary security during that time.
She said she was "hyper aware" of her physical safety for a couple of years, but realised how "precious" it was that MPs could generally go about their business without security.
"It's a real characteristic of politics in this country that politicians are more accessible," Ms Bradford said.
"There's less of a barrier between MPs and the citizen than in many countries and that's really healthy for New Zealand politics."
Ms Bennett said she had suffered serious threats of violence three times.
"One time I managed to get in my car and lock it in time and they just kicked the door," Ms Bennett said.
"That's not New Zealand and it's not the kind of life I want to lead.
"Outside the crazy life we have, I want to lead as normal [of a] life as I possibly can.
"I want to be able to go to the supermarket and walk to work in the morning - I'm going to hold onto that with everything I can."
She sought training on how to keep herself safe from potential threats and said all MPs should be offered that training as part of their induction.
Ms Bradford said the attack on Mr Shaw appeared to have been politically motivated and increased security for MPs needed to be considered.
"It's clear that with our growing population and the intensity of political debate in this time, a greater awareness [of security] by MPs and ministers could be necessary," Ms Bradford said.
A 47-year-old man has been arrested and charged with injuring with intent to injure.
He is due to appear in Wellington District Court today.
The charge carries a maximum penalty of five years in prison.
Mr Shaw expects to return to work today.
