The incident happened at Newham University Hospital shortly after midnight. The victim, a 50-year-old woman, has been treated and discharged.
Police said the attacker used a pair of scissors and a man has been arrested in connection with the incident.
Shane Degaris, deputy group chief executive of Barts Health NHS Trust said: “An emergency department assistant at Newham Hospital was stabbed by a member of the public while at work early this morning.
“This was a shocking and senseless attack on a member of staff doing their duty.”
He said in the wake of the attack there would be a security review.
“The Trust condemns any form of violence and aggression against our dedicated and hard-working staff. In the light of this incident we are reviewing security at all our hospitals to ensure the safety of all our staff and patients at all times,” he added.
“The victim was treated in the Emergency Department, admitted to a ward and has since been discharged home. Police apprehended the perpetrator.”
A statement from Scotland Yard a man was arrested on suspicion of GBH.
This continued: “Police were called at 00:27hrs on Wednesday, 12 June to reports of a stabbing at the Hospital.
“The victim aged 50 suffered multiple stab wounds caused by a pair of scissors. Her injuries have been assessed as non-life threatening.
“The male suspect aged 27 was arrested on suspicion of GBH at the scene. He remains in an east London Police Station where he continues to be questioned.”