Stephanie Clemons Thompson reportedly wrote on Facebook that students should "find compassion" for the "pain" of business student Abdul Razak Ali Artan.
Nearly 1,500 people had signed a petition by Friday morning calling for Ms Thompson to be fired.
Eleven people were injured in Monday's car and knife attack in Columbus.
"I pray you find compassion for his life, as troubled as it clearly was," Ms Thompson wrote, calling Artan a member of the Ohio State University "family".
"Think of the pain he must have been in to feel that his actions were the only solution," the assistant director of residence life wrote in the now-deleted Facebook post.
She went on to condemn students who shared images of Artan's dead body online and "celebrate his death".
The post ended with the hashtags #BlackLivesMatter and #SayHisName.
The petition calling for Ms Thompson's dismissal says: "We cannot allow someone in her influential position to be an apologist to these acts of violent terror.
"Stephanie Clemons Thompson used Facebook as a public platform to shame those who were grateful and relieved the terrorist was taken out so quickly, preventing even more unthinkable terror and destruction in his wake."
Benjamin Johnson, a university spokesman, told the BBC: "This post from this individual clearly is not an official statement of the university and represents her own personal viewpoint."
Authorities believe that Artan, a Somali-born refugee, who lived in Pakistan for seven years before coming to the US, may have self-radicalised online.
The so-called Islamic state claimed him as their "soldier", but authorities say there is no evidence Artan was ever in direct contact with any terrorist organisation.
President-elect Donald Trump earlier this week tweeted that Artan, who arrived in the US with his family in 2014, "should not have been in our country".
An Ohio State University administrator has provoked uproar after expressing sympathy for a student who carried out a campus rampage this week.