"In regard to recent health issues, we wish Scott all the best for a fast and full recovery," Splunk Chief Executive Godfrey Sullivan said in a statement.
Thompson, who had joined Splunk's board in October, was reported to have been diagnosed with thyroid cancer.
Thompson stepped down as Yahoo chief last week, 10 days after activist investor Daniel Loeb accused him of padding his biography by faking a computer science degree.
Last week, Thomson had also resigned from the board of networking gear maker F5 Networks.
Thomson is also a board member of analytics and data management software provider Vertica Systems Inc - owned by Hewlett-Packard Co - and Zuora Inc.
(Reporting by Supantha Mukherjee in Bangalore; Editing by Maju Samuel)