It suggests an event is disruptive or causes problems due to bad timing. His joke came at an inopportune time, overshadowing the serious announcement.
Pro Tip 2/3
Feels Sudden
May imply an event was unexpected and happened without warning. An inopportune storm disrupted our beach wedding.
Pro Tip 3/3
Cultural Sensitivity
Recognize that what's inopportune might vary between cultures or social contexts. Calling late at night could be inopportune in cultures valuing early sleep.