One problem related to manifold/header/muffler/tail pipe has been reported for the 2013 Toyota Prius. The most recently reported issues are listed below.
Engine rattle/knocking noise on first morning start up on occasion. Car is parked outside in a driveway in los angeles, California. Previous dates unknown (maybe happened 4 other times). Log started 11/26/18 since the noise was really bad that day. 11/26/18 at 6 a. M. Car sat in driveway for 2 days. The noise was really bad, the check engine light came on. The next day the check engine light automatically came off. 1/22/19 at 6 a. M. Car sat in driveway for 2 days. The noise was bad but not as bad as 11/26/18. Check engine light did not come on. 2/1/19 at 6 a. M. Car sat in driveway overnight. Slight noise. Check engine light did not come on. I have seen several other complaints online. Some have said its the intake manifold. The dealer has requested I take my car in for the recall (recall no. 18v684) to see if it fixes the problem but I'm going to request they dig into this further. I have approximately 92,000 miles.