And I don't know why people are suddenly outraged by this. Here's some MVP winners from non-playoff teams:
2017: Giancarlo Stanton (NL MVP on a 77-85 team; the runner-up, Votto, was on a 68-94 team)
2016: Mike Trout (AL MVP on a 74-88 team despite a huge year from Mookie on a division winning Sox team)
2015: Bryce Harper (NL MVP)
2009: Joe Mauer (AL MVP, granted the Twins played a Game 163)
2008: Albert Pujols (NL MVP)
2006: Ryan Howard (NL MVP)
2004: Barry Bonds (NL MVP; missed playoffs despite winning 91 games)
2003: Alex Rodriguez (AL MVP; Texas was 71-91)
1997: Larry Walker (NL MVP)
1993: Barry Bonds (NL MVP; the Giants missed the playoffs despite winning 103 games!)
1991: Cal Ripken Jr. (AL MVP)
1989: Robin Yount (AL MVP)
1987: George Bell (AL MVP; Jays won 96 games but missed playoffs) and Andre Dawson (NL MVP; Cubs were 76-85)