Liam Burns had been addressing students at the rally in Kennington Park, south London, when a group of around 15 protesters rushed on stage after chanting "NUS shame on you" and "sell out".
The stage invasion forced Mr Burns to end his speech prematurely and leave the stage. The splinter group, which also threw missiles at Mr Burns during his speech, was then booed by others in the crowd.
One group on the march carried a banner that read "Free education - Smash the NUS".
Speaking after the rally, Mr Burns told Times Higher Education that around 10,000 people joined the protest, which was otherwise peaceful and was held under the slogan "Educate, Employ, Empower".
The march, which ran from Victoria Embankment to Kennington, featured a brief stand off between some protesters seeking access to Parliament Square and police blocking their way.
Mr Burns said: "On the whole the week has been a massive success."
He highlighted a YouGov survey commissioned by the NUS, which found that 58 per cent of parents of children aged 18 or under say MPs who promised to oppose tuition fee hikes should step down at the 2015 election.
Mr Burns said that the polling "proves public sympathy is on our side" and that the protest had also delivered a campaigning boost.
He added that following the protest he had received "floods" of texts from student union officials saying the march was a success and how they planned further action on campus.
On the stage invasion, he said: "I honestly think it's a bit of a distraction. It was about 10 people. They got booed down. I'm not going to lose any sleep."
The stage invaders were "just not representative of students in any way, shape or form", he added.
The rally heard from speakers including Owen Jones, the Independent columnist and author of Chavs: The demonization of the working class, who put the protest in the context of the broader "fight" against the coalition's austerity policies.
He said the 2010 student protests had given "working people" the confidence to say "if they [students] can fight back, we can fight back".
Mr Jones also urged students to "occupy your universities, stand in the... tradition of peaceful civil disobedience".