The twin blasts on Thursday night killed at least 14 people and wounded dozens more in the southern Indian city, raising questions over whether Australia would play the second Test starting on March 2.
"At this stage there is no reason to doubt that what we have planned in Hyderabad next week will go ahead," said Cricket Australia chief executive James Sutherland, who is with the team in Chennai.
"My expectation would be everything would go ahead as planned," he said in a statement released as the opening match in the four-Test series got underway.
Sutherland said he was happy to continue to Hyderabad where the team is scheduled to arrive on Wednesday.
The team were "very comfortable" (with security), everything has gone absolutely to plan".
"We will liaise with the relevant authorities over the course of next few days and make any necessary assessments, but the focus here right now in Chennai is around the cricket," said Sutherland.
"The players are very focused on this Test... no one's indicated concerns at the moment."
The CEO had earlier told Fairfax media that team manager Gavin Dovey had sent players text messages overnight updating them on the blasts and that security had been stepped up.
Dozens of extra police reportedly surrounded the Chennai hotel where the Australian and Indian teams are staying.
Captain Michael Clarke spoke for his players: "From the team's point of view, our focus is wholly and solely on the field because we've got people off the field who are experts in what is going on. We'll be advised by them," he told Fairfax.
"Our thoughts and prayers are with all the people of Hyderabad who have been affected."
Australia pulled out of a tour to Pakistan in 2008 over security concerns after a series of bombings. They also refused to play any matches in the 1996 World Cup in Sri Lanka after bombings there.
Cricket Australia issued a snap statement after the Hyderabad blasts saying the safety of players was paramount but that it had "no information to suggest there is any threat to the team".
The attacks targeted a Hindu district in the city, a hub of India's computing industry in the southern state of Andhra Pradesh.
Australia condemned the bombings "directed at innocent people, going about their daily business."
Foreign Minister Bob Carr said he would write to his Indian counterpart Salman Khurshid to express support for India's efforts to prevent terrorist attacks.
His department also warned Australians following the tour in India that terror attacks could happen anywhere.
"We advise you to exercise a high degree of caution in India at this time because of the risk of terrorism, civil unrest, crime and vehicle accidents," it said.
"Terrorist attacks could occur anywhere at any time in India with little or no warning. Possible targets include public places in New Delhi, Mumbai and other major cities, and Indian security and political interests."
No major international cricket has been played in Pakistan since a deadly attack on the Sri Lankan team bus by armed militants in Lahore in 2009.