Morgan King, a single mother, had apologised to her professor for being absent due to childcare problems.
The University of Tennessee professor emailed to say she could bring her daughter, Korbyn, to lessons and she would be "delighted" to hold her.
Ms King said the warm words made her cry.
In an interviewed with US news channel WBIR-TV, she said: "I just didn't know what else to do. I emailed my professor after class and was apologising for missing class that day."
Professor Sally Hunter, from Knoxville, then wrote back with her "very serious" offer of help.
"Let me know if there are any other ways I could be supporting you," she said, before signing off.
Ms King shared the email on Twitter and it was shared thousands of times.
On Wednesday, the university's chancellor, Beverly Davenport, responded: "Morgan, thanks for showing us challenges college students face. Prof Hunter, thanks for being part of the solution."
Ms King said her professor, who teaches in the Department of Child and Family Studies, is not on Twitter and is nonplussed by the reaction.
"She just doesn't think she did anything special, which speaks about the kind of person she is," Ms King told WBIR-TV.
The student said she has not needed to take her up on the offer yet.
When she graduates she hopes to become a recreational therapist, working with children with disabilities.
"I have to get my degree for Korbyn, not just for me. It means a lot that people are really supportive," Ms King said.
A US student with a three-month-old baby has expressed gratitude to a teacher who offered to babysit so she would not miss classes.