The couple are accused of destroying electronics equipment including a mobile phone and a laptop this week in Georgia, according to TMZ.
A Florida law enforcement official told the website that police were alerted to the alleged incident and arrested both Purvis and Gosa at their home.
The pair have been cited for criminal trespassing and both were released from custody later on $1,300 (£806) bond.
Purvis and Gosa were featured on a 2009 episode of 16 and Pregnant chronicling their attempt to start a life together as teen parents to their son Weston Jr.
16 and Pregnant airs on MTV.