Shyam Das, the president of the Federation of Indian Communities of Queensland, says the community has not taken the comments well and are asking for an explanation from the premier.
"They are offended, very upset," he said, adding the community was questioning why India was singled out.
Mr Das said the border closures were impacting the mental health of his community.
Many people wanted to go to India, he said, whether to bury loved ones or to see their families after a long separation.
"I know someone whose mother passed away, she had to attend the funeral over video," he told SBS News.
"Instead of sympathising with these people, (she's) making them more upset with such comments."
The Australian South Asia Forum said the comments were "uncalled for and must be protested".
A spokesperson for Ms Palaszczuk said the premier was highlighting the problem of approving international travel anywhere, if the federal government didn’t identify which countries Australians could travel to.
"As general examples of countries which unfortunately have had high levels of COVID cases, she mentioned India and Japan, but there are many countries with COVID outbreaks which would similarly make travel problematic," the spokesperson told SBS News in a statement.
"She elaborated further on the difficulties being confronted in Japan.
"The Premier has clearly conveyed Queensland’s sincere best wishes for India, including a $2 million donation to the Red Cross in May this year following a meeting with leaders of the Indian community."