He asked Delhi Police Commissioner Amulya Patnaik to take appropriate action on the June 25 incident, which, he said, also reflected an "elitist mindset".
Rijiju raised the matter with Patnaik after Meghalaya chief minister Mukul Sangma discussed the issue with the minister.
"I will also speak to the urban development ministry on how such privileges can be given to people with such mindsets," he said about the club, which occupies prime land in the heart of the national capital.
"It was a clear case of racial discrimination. Such an elitist mindset of some people will destroy the social fabric of the country," he said.
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The minister of state for home, who is from Arunachal Pradesh, said the incident was "unfortunate and condemnable".
"Action should be taken. Merely issuing a statement is not enough," he said.
The Meghalaya woman, Tailin Lyngdoh, was asked to leave the room because the club's staffers believed her traditional outfit looked like a "maid's uniform", her employer, Nivedita Barthakur Sondhi, told PTI.
Rijiju said Indians often faced discrimination abroad over the colour of their skin.
"Many of us create a hue and cry over such incidents," he said.
The Delhi Golf Club incident, he added, was also a case of racial discrimination.
"It reflected how we treat our own people in our own country," he said.
The club must accept it was wrong and act accordingly, he said, adding that there was "no point" issuing a statement.
"It is unfortunate and regrettable that an undesirable attempt is being made to give the incident a political and cultural overtone," the club said.
It said the club management immediately investigated the incident.
"It has emerged that the incident could have been handled in a much better way by the staff members," it said.
"It was also confirmed that the guests were not asked to leave the club premises," the statement said.
Sondhi said Lyngdoh, who was wearing a jainsem, a traditional Khasi outfit, was asked to leave by two staffers "who told her she looked like a maid and was not allowed there".
In a Facebook post, she had earlier said, "Lyngdoh, an extremely proud, Khasi lady who has travelled the world in her jainsem from London to UAE, was thrown out of The Delhi Golf Club because her dress was taken for a maid's uniform.