How to encourage a student who is a bit shy to engage with the rest of the students?

In this case, as teacher should be able to be a mediator for all students to be engage each other either in classroom or outside too. And as mediator, the teacher should noticed and able to involve the shy student first by direct direction while discussion, fast response with what that student try to speak up and to bring it out in discussion, so she/ he will not loosing a moment of discussion involvement. Thank you.

By grouping with some students and assigning them a task where everybody have to participate to complete that task would a good idea to make a student comfortable with his/her mates.

We can identify the reason by Monitoring closely to that student why He/She shying to engage from other students.

By giving special attention we can encourage the students to be work together with their mates to feel them alike. 

to give them more questions in a classroom. they will fall to answer at the beginning. encourage them to answer after while they will have confidence feeling and they react well. then they will engage to the rest of students. 

There are several ways to address the issue of shyness. I'll list some of them here:

1. Through extra curricular activities.

2. Sports.

3. Group discussions.

4. Rewards.

5. Cheer up.

Teacher can use anyone or all of them which he consider most suitable to the situation. 

Counselling is my first step for the student. Check whether he or has any problem with the students like bullying or any other personal issues running his or her mind. Confidential counselling - to get the student in a comfort zone . Involve him or her in a group activities, may it be a craft works, dramatics,singing .know the area in which he or she is interested . There should be compulsory interactive session at the end of class. Freedom to talk and ask questions in classrooms. even if it's silly. Encourage speaking even if it's not upto the mark. Correct the students in a polite manner. when students are in a comfort zone with teacher they gain more interest to learn from them.

I fully agree with all answers been added.

Positive reinforcement and encouraging the student to practice presentation skills more often would help a lot. A student might rehearse with the teacher before class to feel more confident as confidence is important for classroom participation. 

Multitude of dialogue with him