The event comes less than two months after the Senate rejected a bipartisan proposal to expand background checks for gun purchasers.
The move was seen as a major blow to Obama and his gun control agenda.
The defeat also put the spotlight back on a list of 23 executive actions to combat gun violence released by the White House in January.
One of the actions, none of which need congressional approval, was a national dialogue on mental illness to be led by Sebelius and Duncan.
"We know there is no single solution to the problem of gun violence," Sebelius told a medical conference on Feb. 12.
"But physicians should be able to talk to their patients about guns and gun safety. We can also agree that we need to talk as a society about mental illness."
Participants in Monday's summit will include mental health providers, educators and advocates. Officials from local and state governments, as well as faith leaders, will also attend.