Research by Carol Dweck and other social psychologists shows that students pursue more effective learning strategies when they see intellectual abilities as malleable (i.e., have a growth mindset) rather than innate (i.e., have a fixed mindset). Students with a growth mindset are more willing to learn from mistakes and challenge themselves. It can be helpful to tell students about this research to encourage them to adopt a growth mindset and to acknowledge that a fear of "looking stupid" is common.
Example: "You might be afraid to make mistakes, but mistakes are important!"
See this and related tips as a Tip Sheet: http://csteachingtips.org/tips-for-encouraging-help-seeking