Yes some woman can experience the fetus move as early as 6 weeks so yes it's possible to feel the fetus move inside you as early as 11 weeks although sometimes it doesn't happen until the 12th to 14th week of pregnancy.
When the fetus is moving inside the womb it's also known as Flutters or quickening.
The baby has to develop enough to have arms, legs and a head so as soon as they have those they can cause the feeling of flutters.