The shipment of Krembo, a chocolate-covered marshmallow and cookie, was produced in Gaza and was the first export of processed food from Gaza since 2007.
Qatar says aid to Gaza will continue.
For about two years, Alef and his 28 friends have lived in Kibbutz Kerem Shalom, which is located next to the Gaza border.
The cloth rolls were hidden among other goods that were entering the Hamas-controled enclave.
The shipment and truck were seized and the driver was transferred for questioning by Israel Police.
"Between 85 and 75 tankers of fuel enter the Gaza Strip each week, which helps significantly increase electricity hours. Terrorism prevents you from having that," COGAT's video explained.
Police forces arrived at the scene and detained three suspects.
An Israeli military spokesman noted that there had been "significantly less violence" during Saturday's protest, which organizers had billed a "million person march," than in past weekly demonstrations.
Closure of the crossing comes in the aftermath of Monday’s launch of two incendiary balloons from Gaza into Israel. The balloons exploded in the air and did not cause any damage.