Yes. They have war-slavery, when enemies, captured in battle, become slaves, and sometimes they enslaved lonely travelers.

For example, Ibn Hisham retells a story of Persian boy Salman from Isfahan. He traveled through Arabia and was sold into slavery by his guides from Kalbi tribe. Eventually, he was brought to Medina and asked Muhammad for help.

Muhammad ruled that Salman can buy himself out of slavery, by planting 300 date palms (ثلاث مائة نخلة) for his slaveholder and paying 40 okes of gold (أربعين أوقية) . (Muhammad asked his allies to collect palm shoots and brought his money for to pay the slaveholder.)

Also, pre-Islamic Arabs have slaves of Ethiopian ethnicity, captured in battles. At the time, Ethiopic kingdom waged wars in Arabia, and enemies captured in those wars usually became slaves.

The best known example was Ethiopian slave named Wahshi (غُلَام حَبَشِيّ يُقَالُ لَهُ وَحْشِيّ, ghulaam habbashii yuqaalu la-hu Wahshi), who was promised by Jubayr ibn Mu'tim, that he will be freed from slavery, if he kills Muslim warrior Hamza. Wahshi's story was mentioned in both hadiths and sirah of Ibn Hisham. (And also, there were mentions about Ethiopian slave Bilal, who was tortured by his Pagan Arabic slaveholders for converting to Islam.)