A Madrid police spokeswoman told AFP that officers arrested one person on Thursday morning "for possession of flammable material" after bins were burned at Madrid's Complutense university.
Police also released on bail 54 people who were arrested on Wednesday for burning bins and occupying offices at the Complutense campus in the west of Madrid, the spokeswoman said.
Early on Thursday afternoon, several hundred high school pupils and university students marched noisily but peacefully in central Madrid in a demonstration against the crisis education reforms.
"No to education cuts," they yelled, calling for Education Minister Jose Ignacio Wert to resign over reforms that have seen cuts in spending on schools and universities while higher education fees have been increased.
"It makes me sad because they are not giving everyone the opportunity to study," said one demonstrator, 18-year-old high school pupil Karim Martinez.
"They are raising fees and cutting scholarships. A lot of parents do not have the money to pay for university."
The national Students' Union called for similar demonstrations around the country on Thursday, the second of two days of strikes in high schools and universities.
Spain's conservative government launched spending cuts in 2012 that aimed to save 150 billion euros ($206 billion) to stabilise the public finances of the euro zone's fourth-biggest economy.