Novel treatment options for human papillomavirus (HPV)‐induced cancers are urgently required. The oncogenic transcription factor signal transducer and activator of transcription 3 (STAT3) is considered to be constitutively active in HPV‐positive cervical cancer cells and essential for their proliferation. Moreover, STAT3 was reported to undergo mutually stimulatory interactions with the HPV E6/E7 oncogenes. Thus, inhibiting STAT3 in HPV‐positive cancer cells is under discussion to provide a powerful novel therapeutic strategy. We here show that the antifungal drug ciclopirox destabilizes the STAT3 protein by acting as an iron chelator. However, by exploring the functional consequences of STAT3 inhibition in HPV‐positive cancer cells, we obtained several unexpected results. Chemical STAT3 inhibitors heterogeneously affect cervical cancer cell proliferation and those which act antiproliferative also block the growth of STAT3 knockout cells, indicating induction of off‐target effects. In contrast to several chemical inhibitors, genetic inhibition of STAT3 expression by either RNA interference or the CRISPR/Cas9 method does not appreciably affect cervical cancer cell proliferation. Transcriptome analyses indicate that blocking STAT3 expression in HPV‐positive cancer cells has very limited effects on putative STAT3 target genes. Although the targeted inhibition of specific growth‐promoting signaling pathways leads to a feedback activation of STAT3 in cervical cancer cells via Janus kinase 1/2, this does not lead to treatment resistance. Moreover, we did not obtain experimental evidence for a STAT3‐linked activation of HPV E6/E7 oncogene expression or, vice versa, an E6/E7‐dependent activation of STAT3, at endogenous conditions in cervical cancer cells. Collectively, these findings question the essential role of STAT3 in cervical cancer cell proliferation and the strategy to inhibit STAT3 in these cells for therapeutic purposes.