Inflation data on Tuesday will also provide a glimpse of how much room the authorities have to steer the economy out of its longest spell of sub-5 percent growth in a quarter century.
Annual growth in output from mines, utilities and factories is forecast to accelerate to 5.4 percent in June from 4.7 percent a month earlier, according to a Reuters poll of economists. The output last grew for three months in a row in the July-September quarter last year.
The statistics ministry will release the data at 5:30 p.m.
Weak industrial production is one of the main reasons for India's growth struggle. A fall in output last fiscal year resulted in the second successive year of below 5 percent GDP expansion.
Tuesday's data comes days after infrastructure output growth hit a nine-month high and manufacturing sector posted its fastest growth in 17 months.
It will offer cheer to Prime Minister Narendra Modi who won the strongest electoral mandate in 30 years in May on a promise to revive an economy that is witnessing the longest spell of sub-par growth in a quarter-century.
"The slew of data releases are indicative of green shoots emerging in the economy," economists at Yes Bank wrote in a note.
Modi's election triumph has engendered hopes among Indian businesses that he will replicate his success as the head of the state of Gujarat in speeding up regulatory clearances and stepping up investments.
The Reserve Bank of India (RBI) expects this optimism to translate into economic growth of about 5.5 percent in the fiscal year to March 2015, higher than 4.7 percent last year.
Adding to the growth outlook is a continuing improvement in the global economy, which is expected to boost overseas demand for Indian merchandise and underpin the industrial recovery.
Since taking office, the new leader has sought to boost capital investments through measures such as tax breaks for power projects and higher foreign direct investment caps for railway infrastructure and defence manufacturing.
He is also pushing for the first major revamp in decades of the country's archaic labour laws as part of his plan to revive the economy and create millions of jobs.
While these initiatives will keep the economy on track, a broader revival will remain elusive until Modi gets a handle on India's persistently high inflation.
Runaway prices, especially for food, have squeezed consumer spending that accounts for 60 percent of India's economy.
Retail inflation, which the central bank tracks for setting up its lending rates, eased below 8 percent in June after 28 months hovering above that level. In July, it probably edged up to 7.40 percent from 7.31 percent a month earlier, the poll showed.
Wholesale price-based inflation, meanwhile, is expected to have eased to 5.10 percent last month from 5.43 percent in June.
The RBI wants to reduce retail inflation to 6 percent by 2016. But with a partial drought in some parts of the country pressuring food prices, hitting the inflation target looks tough.
Those concerns forced the central bank to leave interest rates steady last week, dampening hopes for a cut anytime soon.
"Jump in July inflation readings will vindicate the central bank's decision to keep rates on hold and maintain a cautious stance," analysts at DBS Bank wrote in a note.
The government is due to release retail inflation data at 5:30 p.m. on Tuesday and wholesale prices at 12:00 p.m. on Thursday.