She spoke during a visit to Germany by Russian President Vladimir Putin, who has backed a series of investigations into foreign-funded NGOs.
The apparent crackdown has drawn widespread international criticism.
In an interview on German television, President Putin said Russians had a right to know which NGOs were receiving foreign funds "and for what".
Russia passed a law last year requiring all NGOs that receive overseas funding to register as "foreign agents".
It was one of several controversial laws adopted in the aftermath of pro-democracy protests in Moscow.
In her speech to a trade fair in the city of Hanover, Mrs Merkel said Germany wanted to help Russia diversify its economy and innovate.
"We believe this can happen most successfully when there is an active civil society," she said, in the presence of Mr Putin.
"We must intensify these discussions, develop our ideas, and we must give the NGOs, who we know as a motor for innovation, a good chance in Russia."
Mrs Merkel's comments were followed by loud applause. Outside the trade fair, protesters rallied in support of NGOs.
In recent weeks senior EU officials have voiced concern as checks by Russian tax inspectors and prosecutors on foreign-funded NGOs multiplied.
At least two German NGOs - the Konrad Adenauer Foundation (KAS) in St Petersburg and the Friedrich Ebert Foundation (FES) in Moscow - were among those searched.
The KAS think tank is linked to German Chancellor Angela Merkel's Christian Democrats, while the FES is close to Germany's main opposition Social Democrats.
Mr Putin has accused the NGOs of meddling in politics on behalf of foreign powers.
A number of prominent Russian groups say that being labelled as "foreign agents" is insulting, and harks back to Stalin-era purges.
Later on Monday, Mr Putin arrived in Amsterdam, where several thousand gay rights activists had gathered to protest against anti-gay legislation in Russia.
Mr Putin is due to have dinner with Dutch Prime Minister Mark Rutte and to discuss trade links between the two countries.
German Chancellor Angela Merkel has called for Russia to give a chance to non-governmental organisations (NGOs).