The meeting was requested by the United States, France and the United Kingdom -- three of the five permanent members on the Security Council -- as well as Ireland and Albania, the sources said Thursday.
In 2017, the Security Council unanimously passed three sets of economic sanctions after North Korea carried out nuclear and missile tests -- a rare showing of unity for the often gridlocked body.
No joint declaration is expected after Monday's meeting, one diplomat said, although another added that statements are likely to be issued before or afterwards.
The Korean Central News Agency (KCNA), a state media outlet, said Wednesday's missile carried a "hypersonic gliding warhead" that "precisely hit a target 700 km (435 miles) away," without identifying the launcher.
The warhead also demonstrated a "new" capability, moving 120 kilometers laterally after it detached from the launcher to strike the target, it added.
The launch was the second reported test of what Pyongyang claimed were hypersonic gliding missiles, after a similar trial last September.
The United States, Japan and Canada were among those quick to condemn Wednesday's launch, stating that it violated multiple Security Council resolutions and threatened safety in the region as well as the international community.
Pyongyang has argued that the continued development of its weapons technologies is necessary to defend itself against a possible American invasion.