MATTHEW PERRY won’t let his fam­ily watch girlfriend LIZZY CAPLAN’s hit new show, “Masters of Sex,” because he doesn’t want them to see her naked!

The former “Friends” star, who’s been quietly dating the “Mean Girls” actress since 2006, is convinced Lizzy may be “the one,” so he’s prohibited his family from tuning in to the critically acclaimed Showtime series, say sources.

“Matt isn’t a prude, but he doesn’t feel comfortable e with his family seeing Lizzy in the buff,” a close pal told The ENQU IRER.

“He’s very private about his personal life – that’s why he and Lizzy have kept their romance quiet.”

While the 44-year-old actor as dated some of Hollywood’s most gorgeous women, he’s yet to walk down the aisle.

Lizzy, 31, who worked with Matt on his short lived ABC sitcom “Mr. Sunshine” in 2011, play Virginia Johnson in “Masters of Sex,” one -half of the groundbreaking Masters and John­son research team who revolutionized attitudes toward human sexuality in the 1950s.

While Lizzy has no problem getting naked, he’s said to be fine with Matthew protecting her good name within his family.

“Matt’s family knows it’s just acting, but they’re a little old-fashioned., the source noted. “And he really doesn’t want them with the image of naked Lizzy in their heads!”