Auckland Action Against Poverty co-ordinator Ricardo Menéndez said those investigations had the potential to "destroy people's lives".
"Investigators have the ability to reach out to the beneficiary's family members, friends and acquaintances to ask incredibly sensitive questions regarding relationships and sex life.
"The beneficiary is often unaware they are being investigated while MSD contacts these people in their life to obtain information."
Many allegations were found to be unsubstantiated, and several started by vindictive ex-partners calling the anonymous phone line, Menéndez said.
In April it was revealed a woman was told her benefit had been cut off for going on two Tinder dates.
MSD later apologised, saying the case manager had made a mistake about why the woman's benefit was cut.
It said the benefit was suspended because of an allegation the woman was in a long-term relationship, but this was never substantiated.
Menéndez said the group was calling for an end to such investigations, and the law needed to be changed to reflect modern relationships.
"These sort of investigations are able to be carried out due to legislation which can consider two people to be in a 'relationship in the nature of marriage' because they may be dating, sharing accommodation, or engaging in sexual activity."
The law also forced people on benefits to be financially dependent on anyone they considered to be their partner, Menéndez said.
Liz Jones, acting deputy chief executive of service delivery at MSD, said having a few dates has nothing to do with the organisation and shouldn't impact on anything to do with what people are entitled to.
"Many overpayment cases we assess are not cases of criminal fraud. They are simply cases where a client's circumstances have changed and they have not let us know, or haven't let us know before the regular payment cycle has been completed."
Allegations received from the phone line come from a number of sources, Jones said, and lead to a significant proportion of the overpayments identified and prosecuted.
"We administer $24 billion and we have a role to play, where we need to, to ensure if people are receiving money they shouldn't be receiving, that we look into that," Jones said.