Senator Somchai Sawaengkarn said she should take legal action for what he described as a violation of Icelandic law.
Thai netizens, however, are split on the incident, with some supporting the irate chef and others calling his behaviour distasteful.
A Thai man claiming to be the owner of the restaurant live-streamed himself driving Pornthip out of the venue while criticising her work in the Upper house. Somchai, however, confirmed that the man who chased Pornthip out of the restaurant was its chef, not its owner.
The chef had no right to claim to be the restaurant's owner or to chase someone out of it, Somchai said.
Somchai said the incident was a violation of Pornthip's rights. The owner of a restaurant has the right not to serve a customer food, but chasing a customer away and live-streaming the incident on social media is a clear violation of computer-related laws, Somchai said, adding that it is illegal both in Iceland and Thailand.
Somchai said he was not sure whether Pornthip would pursue legal action in Iceland because she would soon return to Thailand.
Netizens have also been questioning why Pornthip was not present at a Senate meeting last week.
Somchai said he was unaware of his colleague's absence from the meeting, but added that it was up to Senate President Pornpetch Wichitcholchai to grant senators leave. He also said her recent trip was personal and not related to any Senate business.