Objectives To assess acceptability of teleconsultation among the socioeconomically marginalized sections of patients with rheumatic and musculoskeletal diseases (RMDs), to identify the socioeconomic barriers in continuing rheumatology care during the COVID-19 crisis and to identify patients who could benefit by shifting to tele-rheumatology consultations. Methods This was a cross sectional analytical study done at a tertiary care teaching hospital in India including patients with RMDs who were not on biological diseases modifying agents. Assessment of disease status, socioeconomic status and economic impact of COVID-19 was done via tele-consultation. Results Out of the 680 patients satisfying inclusion criteria, 373 completed the study. The format was found easy by 334 (89.6%) of them and 284 (76.1%) considered tele-rheumatology better than in-person consultation. During the pre-COVID months, the median monthly per capita income of the families of our patients and cost of illness was Indian rupees (INR) 2000 (US$ 26) and INR 1685 (US$ 21.91), respectively. Families whose financial needs were met (OR = 0.38, 95% CI: 0.239, 0.598) or those with schooling upto at least secondary school (OR = 0.442, 95% CI: 0.260, 0.752) ( P =0.002) were less likely to stop prescription drugs. In a hypothetical model, 289 (77.4%) could be successfully switched to tele-rheumatology follow-up. Conclusion The acceptability of tele-rheumatology among socioeconomically marginalized patients with RMDs is good. During times of crisis, patients from poorer strata of society and lower educational background are likely to abruptly stop medications. Switching to a telemedicine-based hybrid model is likely to improve drug adherence with substantial savings on loss of pay and out of pocket expenditure.