After an appeals court upheld the suspension of the ban, Mrs Clinton, who was defeated by Mr Trump in the November Presidential election, took to Twitter.
The former Democratic candidate trolled Mr Trump by writing “3-0”, referring to the number of times the courts have opposed his plan to ban entry to the US to citizens from Iraq, Iran, Libya, Somalia, Sudan, Yemen and Syria.
— Hillary Clinton (@HillaryClinton) 10 February 2017
Ms Conway, who was Mr Trump’s campaign manager during the election, responded by mocking the failed Democratic candidate.
She tweeted “PA, WI, MI”, referring to the key states of Pennsylvania, Wisconsin and Michigan which Mr Trump took to help secure victory.
It is not the first time Ms Conway and the Clinton’s have clashed on social media.
Last week, Chelsea Clinton criticised Ms Conway for mistakenly referring to the “Bowling Green Massacre”, an alleged attack which never actually took place.
Ms Conway apologised for the error, but sent a response which said: “You can’t ‘invent’ quality candidates either. I misspoke; you lost the election.”