The senator was part of a US delegation visiting the Colombian border city of Cucuta, where humanitarian aid is being stockpiled for planned delivery to Venezuela.
Supporters of Juan Guadio, who the United States and a number of Western countries recognize at the country's rightful president, will distribute the aid.
Around 50 countries, including some 30 European ones, have recognized the interim presidency of Guaido.
Mr Rubio said he was confident that US President Donald Trump's administration would not stand by if the Venezuelan government harmed or imprisoned opposition leader Juan Guaido, who declared himself interim president in January.
Additional storage centers are supposed to open this week in Brazil and Curacao, a Dutch island off Venezuela's northern Caribbean coast.
Venezuela suffers from shortages of food medicine and other daily necessities and also has the worst inflation rate in the world. Ms Hernandez said her mother often "cried from seeing her patients die from lack of medicine".
He spoke a few days after Guaido called on the Venezuelan Armed Forces, supporting President Nicolas Maduro, to change sides, in the anticipation of humanitarian aid arrivals to the crisis-hit country.
Guaido said thousands of Venezuelans have volunteered to meet on February 23 to escort the aid through barricades constructed on an unused bridge that connects the two nations.
The International Committee of the Red Cross (ICRC), in turn, cautioned USA officials against politicising humanitarian assistance and delivering aid without the consent of local authorities.
"Whoever prevents the entry of humanitarian aid is condemned to spend the rest of their lives fleeing global justice, because that is an worldwide crime", Mr Rubio said in Spanish.
Venezuelans based in Miami held their own drive, putting together 1,000 crates of food to send to their homeland.
Mr Guaido appealed for the military to let the aid pass.
For analyst Benigno Alarcon, "as the regime closes the door on humanitarian aid, it closes it to a peaceful solution to the political situation in the country". Rodriguez did not announce the artists that are expected to perform, saying only that it would be massive.