Yes, William Shakespeare was indeed a contemporary figure in the 16th century.

• Born: Approximately April 23, 1564 Shakespeare Birthplace Trust
• 16th Century: 1501 to 1600

Shakespeare's birth in 1564 falls squarely within the 16th century. He began to gain prominence as a playwright and poet towards the late 16th century, with many of his early works being written and performed before 1601.