The arrested suspects were to remain in custody for at least four days while the authorities conduct an investigation into the accident, the state-run MENA news agency reported.
Seven Australians, four French nationals, two South Africans, two Argentinians and a Brazilian were also among those injured.
The mother of one of the Australians on board says the pilot was knocked out while the balloon was in the air.
Zoe Drinkwater from Newcastle was one of the passengers, according to the Seven Network, who spoke to her mother on Saturday.
"As they were coming in to land there was a big gust of wind that came up which then consequently knocked out the pilot," Lainie Drinkwater said.
"The pilot was unconscious ... so no-one was actually steering and operating this balloon so it was just plunging."
Vanessa Condran, from the Illawarra region, 31, posted on Facebook: "I am alright, a few bumps and bruises.
"And probably will never set foot in another hot air balloon ever again. I feel lucky to have walked out of this traumatic experience, a scary freak accident."
Melbourne's Adele Jayde posted on Instagram that she was "extremely thankful and blessed that myself and my travel companions on this tour all managed to come out of it alive with only minor injuries, as others in the basket with us weren't so lucky."
News Corp Australia named the other four Australians involved as Melbourne pair Montanna Leveque, 20, and River Kano, 21, 24-year-old Emma Forster from Alice Springs and Morgan Adams of Victoria.
Hany Al-Sayyed, traffic manager for the Sinbad hot air balloon company, told CNN the balloon was getting ready to land when a sudden, strong wind erupted.
"The victim is an Australian man of South African descent. His head was hit during the landing. Most of the other injuries are minor, scratches to the torso, and they were taken to the hospital," he said.
Some of those onboard were on a Topdeck tour. A spokesperson from the travel company's London headquarters said last night that response teams were assisting travellers.
Egypt's Civil Aviation Ministry said other balloons carrying over 400 tourists had taken off and landed safely on Friday.
Balloon flights were resumed on Saturday.
Luxor has a history of hot air balloon crashes. The deadliest was in 2013 when at least 19 foreign tourists were killed when theirs caught fire.
- additional reporting AP
