Finnegan landed on the paternity list Tuesday, Mark Zuckerman of MASNSports.com reports.
Finnegan has emerged as the Nationals' primary closer, saving six games in his last 13 appearances while allowing just a single earned run in 12 innings over that stretch. No other National has recorded a save since Brad Hand was dealt to the Blue Jays at the deadline, so the next man up in Finnegan's absence isn't obvious. Among the relievers currently on the roster, Mason Thompson, Austin Voth and Wander Suero (who was recalled to take Finnegan's roster spot) have appeared in the highest-leverage situations this season. Finnegan should return no later than Friday.