Solano, who had two successful spells on Tyneside as well as stints with Aston Villa, West Ham, Leicester and Hull, was detained by local police on Thursday.
The former midfielder claimed he had left his home before the 8pm curfew - but was delayed when lunch overran.
"I obviously regret this very much and I ask for forgiveness," Solano told radio station RPP Noticias. "I am not going to justify it. It's very tough for everyone but the most important thing is our health, without that we can't do anything."
Solano, now the assistant coach of the Peruvian national team, was taken to a Lima police station after a neighbour spotted him and complained but he was released shortly afterwards, according to local media.
The 45-year-old has since alleged he was set up by a television show.
Peru has reported 580 confirmed cases and nine deaths so far from Covid-19.