"We're really happy, but now the real work begins. It's an important but small step," Lena Nyhus, member of the Intact Denmark group that initiated the petition, told news agency Ritzau.
Although Denmark's Socialist People's Party has expressed its support for the petition, other primary political parties in the country have not expressed the same sentiment.
If passed, the ban would mandate a six-year prison sentence for anyone who carries out a circumcision on a male under the age of 18, unless there is a valid medical reason.
Since 2003, the same punishment has existed for carrying out female genital mutilation in Denmark.
"Society has a special obligation to protect the fundamental rights of the child until they've reached an age and maturity where they can take on this responsibility themselves," the petition reads.
According to Danish health officials, between 1,000 and 2,000 circumcisions take place each year in the country. The practice of removing a male child's foreskin is common among those of the Jewish and Muslim faiths.
The Jewish community in Denmark has protested the petition, stating that the practice has been performed in Denmark for over 400 years.