Pence and others involved in the Republican presidential campaign last year criticised Clinton's use of a private email server during her time as U.S. Secretary of State.
Clinton was on an airplane traveling from Boston to New York on Friday when a fellow passenger snapped a photo of her glancing down at Friday's USA Today newspaper front page headline "Pence used personal email in office".
Pence's use of an AOL email account was first reported by the Indianapolis Star on Thursday. It said Pence used the account, which was hacked last summer, at times to discuss sensitive matters and homeland security issues while he was governor of Indiana.
Pence said on Friday he had complied with Indiana laws in his use of the email account, and he had an outside attorney review his private email records and archive those related to state business.
During the campaign, U.S. President Donald Trump and Pence said Clinton's use of a private server broke the law and endangered national security - complaints that led their supporters to chant "Lock her up!" at rallies.
The State Department's internal watchdog said Clinton's use of a private server broke department rules. The FBI reviewed her emails for classified material, but it found that no criminal charges were warranted.