It would make sense at first glance since it would differentiate Han women from Manchu ones, but the Qing dynasty had made Manchu fashion compulsory for all Chinese men with the hair queue and Manchu robes for officials so why did they allow the practice to continue?
The Qing Dynasty did attempt to ban footbinding, but was ultimately unsuccessful. Even before the Manchus entered China, the official policy was to ban any non-Manchu clothing and practices. For instance, in 1638(崇德三年)the Manchu emperor Hongtaiji issued an order that banned the practice . Here is the original text:
若有效他國衣帽,及令婦女束髮裹足者,是身在本朝,而心在他國也,自今以後,犯者俱加重罪.
Footbinding was considered as a sign of disloyalty as it did not conform with Manchu customs. When the Manchus entered China in 1644(順治元年),the queen Xiao Zhuang( 孝莊皇后)issued a
similiar order. Here is the text:
有以纏足女子入宮者斬.
The translation is: those who enter the imperial harem with binded feet shall be executed.
In the second year(1645), the Qing court issued an order that banned footbinding within the general populace as well. Here is the text:
所生女子禁纏足.
The translation would be : any newborne women from now on shall be banned from binding their feet.
As for detailed punishment for non abidance, it was very severe. In 1661(順治十七年). the Qing emperor ordered that:
有抗旨纏足者,其夫或父杖八十,流三千里.
if a women was found to be footbinding, her father shall be caned eighty times and exiled.
This order is still repeated when the next emperor, Kangxi replaced Shunzhi after his death.
In 1664(康熙三年), the emperor laid down even more severe punishment for footbinding. Here is the text:
康熙元年以後所生女子違法裹足,其父有官者,交吏兵二部議處;兵民之家,交刑部,責四十板流徙;十家長不行稽察,枷號一月,責四十板;該管督撫以下文職官員,有疏忽失於覺察者,聽吏兵二部議處 Here is the rough translation. For those who were found to be binding their feet, if her(foot biding woman) father is a civil official,. then he will face court-marshalled; if her father is a soldier or an ordinary citizen, he will face a trial, be caned fourty times and exiled. The parents will be locked to the chains for one month and caned fourty times. The civil official of that region will be penalised as well. However these measures seem to be ineffective or not observed as footbiding was still common practice. In fact. the civil officials petitioned the emperor to re-allow foot binding. in 1651 (康熙七年) the ban was lifted. One thing to note is that while the punishment for foot binding was severe, it was relatively lax, considering that the Qing court threatened the summary execution and extermination of cities if its citizens refused to shave their heads. (一人不剃全家斬,一家不剃全村斬) On top of that Manchu and Hakka women didnot bind their feet. TLDR: yes there was a ban, but it was given up shortly afterwards.
Reference: 清太宗實錄 淸稗類抄 高洪興(2004)纏足史
PS, this is my first post here on AskHistorians. Therefore if the mods here find my response unsatisfactory or not following the community standards, please feel free to delete and notify me!