Background/Objectives: One of the major risks associated with the concomitant use of herbal products and therapeutic drugs is herb–drug interactions (HDIs). The most common mechanism leading to HDIs is the inhibition and/or induction of transport proteins and drug-metabolizing enzymes by herbal ingredients, causing changes in the pharmacokinetic disposition of the victim drug. The present study aimed to determine the potential interactions of Uncaria tomentosa (UT) (cat’s claw), a popular herb due to its supposed health benefits. Methods: The effect of UT extract and its major oxindole alkaloids was investigated on multispecific solute carrier (SLC) and ATP-binding cassette (ABC) drug transporters, using SLC transporter-overexpressing cell lines and vesicles prepared from ABC transporter-overexpressing cells. Results: UT extract significantly inhibited all ABC transporters and the majority of the SLC transporters tested. Of the investigated oxindole alkaloids, isopteropodine significantly inhibited OATP, OCT1 and OCT2, OAT3, ENT4, MDR1, and BCRP transporters. OCTs, OCTN1-, ENT1-, and MDR1-mediated substrate accumulation was below 50% in the presence of mitraphylline. Conclusions: Based on the calculated intestinal concentration of UT extract, interactions with intestinal transporters, especially OATP2B1, ENTs, MRP1, MRP2, MDR1, and BCRP could be relevant in vivo. Our data can help to predict the clinical consequences of UT co-administration with drugs, such as increased toxicity or altered efficacy. In conclusion, the use of these in vitro models is applicable for the analysis of transporter-mediated HDIs similar to drug–drug interaction (DDI) prediction.