The decision was taken after a meeting between Israel and Qatar, aided by Egyptian officials and the UN Special Coordinator for the Middle East Peace Process.
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.
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.
According to the Gaza Economy Ministry, Israeli products account for 65% of all items imported into Gaza.
Israel has threatened to assassinate high-ranking Hamas members if the violence along the Gaza Strip border continues.