Yes, Indian citizens must have a valid visa to enter Kyrgyzstan. They can easily apply for an e-visa online, which is issued for tourism, including visiting friends and receiving medical services, without engaging in paid or profit-making work.
Note: Indian citizens holding a long-term multiple-entry visa from the USA, Great Britain and the Schengen Zone are allowed to enter and stay in the Kyrgyz Republic without a visa for up to 7 days.