The 24-year-old dancer - who is believed to have been dating Lopez, 42, since November - alluded to their romance in a message urging followers to start "indulging passion and dreams".
"Age, status, n opinions of others are irrelevant. Our hearts are endless and our souls infinite," he wrote. "Our ages are mere reminders of the hours logged on this earth and the precious time remaining.
"We should all honour our time here by indulging our passion and dreams. So, close your ears and open your hearts; Love and be happy! (sic)"
On why he wrote the message, Smart added: "[A] good friend sent it for me and thought it was beautiful and perfect!!! #truth."
Lopez has refused to comment on rumours that she is dating Smart, though the pair have been seen together in public numerous times - including on trips to Hawaii and Morocco.
The 'Papi' singer separated from husband Marc Anthony in July 2011.
> Jennifer Lopez, Marc Anthony clash as kids call Casper Smart 'daddy'
Watch Jennifer Lopez in the video for 'Papi' below: