He said it appeared that a motorcycle rider came from behind and attached an explosive device to the back door of the diplomat’s car.
Iran has denied Israeli accusations that it was behind the attacks.
Three other people were injured in the Delhi blast.
“The investigations are on,” Mr Chidambaram told reporters after meeting the city police chief and other officials on Tuesday morning.
“We believe it was a very well-trained person who committed the attack and that the target was the Israeli diplomat’s wife.
The minister said that the police were scanning the closed-circuit camera footage, “but we have no clear images of the bike or the the biker yet”.
Mr Chidambaram said they were “not pointing fingers at anyone or any group yet, but we condemn the attack in the strongest terms”.
Indian officials have been in touch with Israeli officials and “we have assured them that India will find the perpetrators”, he said.
Security at Israeli embassies has been tightened in recent months following warnings of potential attacks, after Iran accused Israel of a series of attacks on its nuclear scientists.
BBC security correspondent Gordon Corera said one of them, Mostafa Ahmadi-Roshan, died last month when motorcyclists placed a “sticky bomb” on his car – a technique similar to that used in previous attacks attributed to the work of Israel’s Mossad.
Similarities seen in the Delhi blast could be an indication of the aggressors sending a message that attacks in Tehran will be repaid in kind, he added.